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1
Badinski, Alexander Nikolai. "Forces in quantum Monte Carlo". Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612494.
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Hine, Nicholas. "New applications of quantum Monte Carlo". Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446023.
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Poole, Thomas. "Calculating derivatives within quantum Monte Carlo". Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/29359.
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Quantum Monte Carlo (QMC) methods are powerful, stochastic techniques for computing the properties of interacting electrons and nuclei with an accuracy comparable to the standard post-Hartree--Fock methods of quantum chemistry. Whilst the favourable scaling of QMC methods enables a quantum, many-body treatment of much larger systems, the lack of accurate and efficient total energy derivatives, required to compute atomic forces, has hindered their widespread adoption. The work contained within this thesis provides an efficient procedure for calculating exact derivatives of QMC results. This procedure uses the programming technique of algorithmic differentiation (AD), which allows access to the derivatives of a computed function by applying chain rule differentiation to the underlying source code. However, this thesis shows that a straightforward differentiation of a stochastic function fails to capture the important contribution to the derivative from probabilistic decisions. A general approach for calculating the derivatives of a stochastic function is presented, where a similar adaptation of AD applied to the diffusion Monte Carlo (DMC) algorithm yields exact DMC atomic forces. The approach is validated by performing the largest ever DMC force calculations, which demonstrate the feasibility of treating systems containing thousands of electrons. The efficiency of AD also enables molecular dynamics simulations driven entirely by DMC, adding new functionality to the QMC toolkit. Another focus of this thesis is using the phenomenon of stochastic coherence to correlate DMC simulations, allowing finite difference derivatives to be obtained with a small error. Whilst this method is far easier to implement than AD, preliminary results show an instability when treating larger systems. A different approach is obtained from extrapolating this method to a finite difference step size of zero, producing algebraic expressions for a direct differentiation of the DMC algorithm.
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Seth, Priyanka. "Improved wave functions for quantum Monte Carlo". Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/244333.
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Quantum Monte Carlo (QMC) methods can yield highly accurate energies for correlated quantum systems. QMC calculations based on many-body wave functions are considerably more accurate than density functional theory methods, and their accuracy rivals that of the most sophisticated quantum chemistry methods. This thesis is concerned with the development of improved wave function forms and their use in performing highly-accurate quantum Monte Carlo calculations. All-electron variational and diffusion Monte Carlo (VMC and DMC) calculations are performed for the first-row atoms and singly-positive ions. Over 98% of the correlation energy is retrieved at the VMC level and over 99% at the DMC level for all the atoms and ions. Their first ionization potentials are calculated within chemical accuracy. Scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values are also evaluated. A form for the electron and intracule densities is presented and fits to this form are performed. Typical Jastrow factors used in quantum Monte Carlo calculations comprise electron-electron, electron-nucleus and electron-electron-nucleus terms. A general Jastrow factor capable of correlating an arbitrary of number of electrons and nuclei, and including anisotropy is outlined. Terms that depend on the relative orientation of electrons are also introduced and applied. This Jastrow factor is applied to electron gases, atoms and molecules and is found to give significant improvement at both VMC and DMC levels. Similar generalizations to backflow transformations will allow useful additional variational freedom in the wave function. In particular, the use of different backflow functions for different orbitals is expected to be important in systems where the orbitals are qualitatively different. The modifications to the code necessary to accommodate orbital-dependent backflow functions are described and some systems in which they are expected to be important are suggested.
5
Leung, Wing-Kai. "Applications of continuum quantum Monte Carlo methods". Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411231.
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Brown, M. D. "Energy minimisation in variational quantum Monte Carlo". Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596975.
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After reviewing previously published techniques, a new algorithm is presented for optimising variable parameters in explicitly correlated many-body trial wavefunctions for use in variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) calculations. The method optimises the parameters with respect to the VMC energy by extending a low-noise VMC implementation of diagonalisation to include parameters which affect the wavefunction to higher than first-order. Similarly to minimising the variance of the local energy by fixed-sampling, accurate results are achieved using a relatively small number of VMC configurations because the optimisation is based on a least-squares fitting procedure. The method is tested by optimising six small examples intended to broadly cover the range of systems and wavefunctions typically treated using VMC and DMC, including atoms, molecules, and extended systems. Least-squares energy minimisation is found to be stable, fast enough to be practical, and capable of achieving lower VMC energies than minimisation of the filtered underweighted variance of the local energy (and the underweighted mean absolute deviation from the median local energy) by fixed-sampling. Least-squares energy minimisation is used to optimise four different wavefunctions for each of the all-electron first row atoms, from lithium to neon: single-determinant Slater-Jastrow wavefunctions with and without backflow transformations, and multi-determinant Slater-Jastrow wavefunctions with and without backflow transformations. The optimisations are more stable and successful than some previous variance minimisations using similar wavefunctions. The DMC energies of the energy-optimised wavefunctions for the atoms from boron to neon are significantly lower than previously published results, and, using the multi-determinant Slater-Jastrow wavefunctions with backflow, the calculations recover at least 90% of the correlation energies for lithium, beryllium, boron, carbon, nitrogen and neon, 97% for oxygen, and 98% for fluorine.
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Williamson, Andrew James. "Quantum Monte Carlo calculations of electronic excitations". Thesis, University of Cambridge, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627604.
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Kent, Paul Richard Charles. "Techniques and applications of quantum Monte Carlo". Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624448.
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Kunert, Roland. "Monte Carlo simulation of stacked quantum dot arrays". [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981321399.
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Gillies, Patrick R. "Path integral quantum Monte Carlo for semiconductor nanostructures". Thesis, Heriot-Watt University, 2007. http://hdl.handle.net/10399/2033.
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Path integral quantum Monte Carlo (PI-QMC) is a powerful technique, which can be used to model the properties of multiple interacting particles at finite temperatures. In this work path integral quantum Monte Carlo has been applied to the problem of few particle interactions in quantum dots and other semiconductor nanostructures. Quantum dots are currently the subject of much research and in order to further understand their properties it is necessary to perform theoretical modelling. In this work, the method by which the problem of the attractive Coulomb potential was overcome is detailed. Following that, comparisons are made between . experimental data and PI-QMC results for excitonic complexes in 111-V dots. Both the energies and voltage extents were found to show good agreement between experiment and theory. Comparisons are also between theory and experiment of II-VI, with experimental data using a harmonic potential to model the dot. Again, good agreement is seen. Finally, as an example of the power of PI-QMC, the behaviour of electrons and holes is modelled for alternative nanostructures, such as coupled quantum dots, quantum rings and core-shell structures. With some simple modifications, the same PI-QMC method could be used.
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Kenny, Steven David. "Relativistic quantum Monte Carlo calculations for electronic systems". Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389850.
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Nail, Graeme. "Quantum chromodynamics : simulation in Monte Carlo event generators". Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/quantum-chromodynamics-simulation-in-monte-carlo-event-generators(46dc6f2e-1552-4dfa-b435-9608932a3261).html.
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This thesis contains the work of two recent developments in the Herwig general purpose event genrator. Firstly, the results from an new implementation of the KrkNLO method in the Herwig event generator are presented. This method allows enables the generation of matched next-to-leading order plus parton shower events through the application of simple positive weights to showered leading order events. This simplicity is achieved by the construction Monte Carlo scheme parton distribution functions. This implementation contains the necessary components to simulation Drell-Yan production as well as Higgs production via gluon fusion. This is used to generate the first differential Higgs results using this method. The results from this implementation are shown to be comparable with predictions from the well established approaches of POWHEG and MC@NLO. The predictions from KrkNLO are found to closely resemble the original configuration for POWHEG. Secondly, a benchmark study focussing on the source of perturbative uncertainties in parton showers is presented. The study employs leading order plus parton shower simulations as a starting point in order to establish a baseline set of controllable uncertainties. The aim of which is to build an understanding of the uncertainties associated with a full simulation which includes higher-order corrections and interplay with non- perturbative models. The uncertainty estimates for a number of benchmark processes are presented. The requirement that these estimates be consistent across the two distinct parton show implementations in Herwig provided an important measure to assess the quality of these uncertainty estimates. The profile scale choice is seen to be an important consideration with the power and hfact displaying inconsistencies between the showers. The resummation profile scale is shown to deliver consistent predictions for the central value and uncertainty bands.
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Pearson, Sean. "Quantum dot studies with path integral Monte Carlo". Thesis, University of Leicester, 1995. http://hdl.handle.net/2381/35762.
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The purpose of this thesis is to investigate the properties of semiconductor quantum dots by applying a quantum Monte Carlo technique. In the quantum mechanical regime such systems exhibit a range of fascinating and potentially useful phenomena. It is found that path integral Monte Carlo is generally a powerful technique for evaluating finite temperature properties of quantum many-body systems. The method is outlined for the treatment of a single-particle system. The generalisation to N particles is explained while the appropriate symmetry of the wave functions is incorporated for identical particles. Inherent numerical problems which arise for fermions are considered. An efficient new method is introduced which significantly reduces the statistical errors for large numbers of fermions. The Monte Carlo procedure is adapted to allow the calculation of magnetic field dependent quantities. The question of the existence of a molecular analogue to a Wigner crystal in a quantum dot is investigated. The phase diagram for the six-electron system studied exhibits an ordered phase in the regime of weak electrostatic confinement and low temperature. The melting temperature of this phase is found to be enhanced by the presence of a perpendicularly applied magnetic field. The dimensionality of quantum dots is considered. The two-electron ground state undergoes a transition as the crossover between three and two dimensions is effected.
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Malone, Fionn Dara. "Quantum Monte Carlo simulations of warm dense matter". Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/53379.
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Recent experimental progress in laser technology has led to renewed interest in warm dense matter. Found in the interiors of gas giants and in inertial confinement fusion experiments, warm dense matter is relevant to problems of fundamental and technological importance but is a challenge to create experimentally and describe theoretically. Modern electronic structure theory, in the form of density functional theory coupled with molecular dynamics, in principle offers a route to describing realistic warm dense matter. However, until quite recently, no accurate exchange correlation free energy functionals existed and the accuracy of existing fits was largely unknown. %Moreover, existing accurate quantum Monte Carlo data for the exchange correlation energy of the warm dense electron gas differ substantially. In this thesis we extend the independent, systematically exact, density matrix quantum Monte Carlo method, to address these issues. Focussing on the warm dense uniform electron gas, we first outline how sampling issues present in the original formulation can be overcome and how numerical basis set corrections can significantly reduce the computational burden at high electronic temperatures. We next introduce a systematic approximation allowing larger system sizes to be tackled. In the process we resolve a controversy present between two competing path integral Monte Carlo methods, whose results for the exchange correlation energy of the uniform electron gas differ substantially in the warm dense regime. Finally, we develop a general procedure for deriving analytic finite size corrections in the warm dense regime, thus removing the final barrier to reaching the thermodynamic limit.
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Mostaani, Elaheh. "Quantum Monte Carlo study of low dimensional materials". Thesis, Lancaster University, 2016. http://eprints.lancs.ac.uk/78989/.
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This thesis addresses several challenging problems in low-dimensional systems, which have rarely or never been studied using quantum Monte Carlo methods. It begins with an investigation into weak van der Waals-like interactions in bilayer graphene and extends to graphene placed on top of boron nitride at four different stacking configurations. The in-plane optical phonon frequencies for the latter heterostructure as well as the out-of-plane phonon frequencies for both structures are calculated. We find that the binding energies (BEs) of these structures are almost within the same range and are less than 20 meV/atom. Although the phonon vibrations are comparable within both the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT), DFT gives quantitatively wrong BEs for vdW structures. Next, the BEs of 2D biexcitons are studied at different mass ratios and a variety of screening lengths. Our exact DMC results show that the BEs of biexcitons in different kinds of transition-metal dichalcogenides are in the range 15 − 30 meV bound at room temperature. Besides 2D systems, the electronic properties of 1D hydrogen-terminated oligoynes and polyyne are studied by calculating their DMC quasiparticle and excitonic gaps. By minimising the DMC energy of free-standing polyyne with respect to the lattice constant and the bond-length alternation, DMC predicts geometry in agreement with that obtained by accurate quantum chemistry methods. The DMC longitudinal optical phonon is within the range of experimental values. Our results confirm that DMC is capable of accurately describing Peierls-distorted materials.
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Himberg, Benjamin Evert. "Accelerating Quantum Monte Carlo via Graphics Processing Units". ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/728.
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An exact quantum Monte Carlo algorithm for interacting particles in the spatial continuum is extended to exploit the massive parallelism offered by graphics processing units. Its efficacy is tested on the Calogero-Sutherland model describing a system of bosons interacting in one spatial dimension via an inverse square law. Due to the long range nature of the interactions, this model has proved difficult to simulate via conventional path integral Monte Carlo methods running on conventional processors. Using Graphics Processing Units, optimal speedup factors of up to 640 times are obtained for N = 126 particles. The known results for the ground state energy are confirmed and, for the first time, the effects of thermal fluctuations at finite temperature are explored.
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Amir-Azizi, Siamak. "Linear filtering algorithms for Monte Carlo simulations". Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280859.
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Memis, Sema. "Ensemble Monte Carlo Modeling Of Quantum Well Infrared Photodetectors". Phd thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/2/12607291/index.pdf.
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Quantum well infrared photodetectors (QWIPs) have recently emerged as a potential alternative to the conventional detectors utilizing low bandgap semiconductors for infrared applications. There has been a considerable amount of experimental and theoretical work towards a better understanding of QWIP operation, whereas there is a lack of knowledge on the underlying physics. This work provides a better understanding of QWIP operation and underlying physics through particle simulations using the ensemble Monte Carlo method. The simulator incorporates Gamma, L, and X valleys of conduction band as well as the size quantization in the quantum wells. In the course of this work, the dependence of QWIP performance on different device parameters is investigated for the optimization of the QWIP structure.
The simulations on AlGaAs/GaAs QWIPs with the typical Al mole fraction of 0.3 have shown that the L valley of the conduction band plays an important role in the electron capture. A detailed investigation of the important scattering mechanisms indicates that the capture of the electrons through the L valley quantum well (L-QW) affects the device performance significantly when Gamma and L valley separation is small. The characteristics of electron capture have been further investigated by repeating the simulations on QWIPs for quantum well widths of 36 and 44 Å. The results suggest that the gain in the shorter well width device is considerably higher, which is attributed to the much longer lifetime of the photoexcited electrons as a result of lower capture probability (pc) in the device. The effects of the L-QW height on the QWIP characteristics have also been studied by artificially increasing this height from 63 to 95 meV in Al0.3Ga0.7As/GaAs QWIPs. The increase in the L valley (L-QW) height resulted in higher pc and lower gain due to high rate of capturing of these electrons when Gamma and L valley separation is small.
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Drummond, N. D. "Application of quantum Monte Carlo methods to electronic systems". Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598657.
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This thesis is concerned with the development and application of quantum Monte Carlo (QMC) methods for calculating the energies of atoms, molecules and solids from first principles. Several modifications to the variational and diffusion Monte Carlo (VMC and DMC) methods are investigated. It is shown that biases due to the use of finite time steps largely cancel when the ionisation energy of neon is calculated. A new form of trial wave function, which is more flexible and computationally efficient than existing forms, is proposed for use in QMC simulations. Results obtained with the new trial wave function are analysed and discussed. The results of an investigation into some aspects of a class of QMC methods in which the computer time is proportional to the square of the number of particles simulated are given. It is found that the least biased method of truncating localised orbitals is to cut them off abruptly. The results of applying QMC methods to two different electronic systems are presented: (i) An accurate calculation of the density at which a three-dimensional uniform gas of electrons will crystallise at zero temperature is described. The DMC energy of the crystalline phase is evaluated at different densities, and the point at which the energy curve crosses that of the fluid phase is located. (Accurate energy data for the fluid phase are already available). The transition density is found to be rs = 106 ± 1 a.u. (ii) DMC calculations of the optical gaps of various nanometre-sized diamond molecules are reported. It is found that molecules which are smaller than about 1 nm have larger optical gaps than bulk diamond. These quantum-confinement effects are not found to be present in molecules with diameters in excess of 1 nm. The electron affinity of C29H36 is found to be negative.
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Booth, G. H. "A novel quantum Monte Carlo method for molecular systems". Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596772.
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This thesis is concerned with the development of a new ab initio Monte Carlo method for the evaluation of exact, basis set correlation energies. A simple set of rules acting on signed walkers allow for the simulation of the underlying imaginary-time Schrödinger equation in a finite space of Slater determinants. These rules return probabilistic events which are stochastically realised in each step of the algorithm. The antisymmetric space in which the dynamic operates precludes the emergence of Bosonic solutions, and the Fermion sign problem is countered without approximation by inclusion of annihilation events between walkers of different sign. The method is applied to many molecular systems described by common Gaussian basis sets. Single point calculations, binding curves, basis set expansions and detailed studies of ionisation potentials are included. In these investigations, the method is compared to several alternative quantum chemical methods as well as exact full configuration interaction results to asses its qualities. The method is found to significantly reduce the memory and CPU requirements compared to exact diagonalisation methods, and includes an effective parallelisation scheme which scales almost linearly up to thousands of processors. This extends the scope of exact multireference calculations and allows for larger systems than previously possible to be treated.
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鄒鳳嬌 i Fung-kiu Chow. "Quantum statistical mechanics: a Monte Carlo study of clusters". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31224258.
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Benoit, David Michel. "Diffusion Quantum Monte Carlo simulations of hydrogen-bonded clusters". Thesis, University College London (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313057.
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Wilson, Marcus Thomas. "Auxiliary field quantum Monte Carlo calculations for exotic jellium". Thesis, University of Bristol, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.281607.
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Saritas, Kayahan. "Quantum Monte Carlo for accurate energies and materials design". Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/111252.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 107-119).
Quantum Monte Carlo (QMC) is an electronic structure calculation method that is capable of calculating incredibly accurate solutions of Schrödinger equation of quantum mechanics for real systems. However, QMC is computationally very expensive compared to density functional theory (DFT) method, such that its application has been limited. In addition, QMC is a stochastic (Monte Carlo) method, meaning that the way calculations are initialized, where a lot of user effort is invested, is crucial for getting accurate results. Computational expense can be justified if the data would be used repeatedly, however the lack of automatization is a severe problem, if QMC would be used in materials discovery. In Chapter 4, we show our automated calculation strategy for formation energy of periodic materials using QMC. We show that our method performs almost by an order of a magnitude more accurate, compared to high throughput DFT strategies having empirical corrections. Nevertheless, it would be beneficial to understand when DFT methods fail such that QMC is used only when the computational expense is justified. A single DFT functional rarely performs uniformly accurate accross different materials and properties due to nonsystematic errors. In Chapter 5, we investigate one specific example: dihydroazulene ring opening photoisomerization, where different substitutions on the ring opening moiety introduce isomerization enthalpy errors up to 0.8 eV. We show that GGA exchange is the main reason for failure in B3LYP, PBE and TPSSH functionals. However, performing a test, similar to the Chapter 5, on each chemical reaction can be an intimidating task where the benchmark set must be carefully devised by an expert in the field. In the absence of experiments, the DFT functional choice is still often done in heuristic way. In Chapter 6, we demonstrate how we can systematically analyze benchmark sets using machine learning to provide highly accurate reaction energies and provide DFT functional selection for different classes of materials when high accuracy calculations or experiments are not available. Our approach provides probabilities of getting accurate results for a reaction that is investigated using each DFT functional.
by Kayahan Saritas.
Ph. D.
25
Vigor, William Andrew. "Investigating quantum Monte Carlo methods in Slater determinant bases". Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/42987.
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In this thesis we investigate the recently developed Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method. This method, unlike the traditional methods in Quantum Monte Carlo (QMC), doesn't require the use of the uncontrolled fixed node approximation and so potentially it can yield far more accurate results. This means that it can be thought of as a hybrid between the methods used by quantum chemists and QMC, and thus has spawned a new field of stochastic quantum chemistry. The work described in this thesis can be split into three distinct but interrelated parts. We begin with an investigation of the underlying FCIQMC stochastic process. We show that FCIQMC is an example of Markov Chain Monte Carlo. This means we can compute a stochastic matrix from which all details about the Monte-Carlo simulation can be obtained. Unfortunately the size of the space scales unfavourably as a function of system size meaning that we have only managed to compute the matrix for the smallest interesting two determinant system. We then use these results to quantify population control bias in FCIQMC for a two determinant system supplementing these analytical results with empirical results to investigate more realistic systems. We then attempt to quantify the efficiency of the FCIQMC algorithms, defining a measure of efficiency. After this we investigate the dependence of our measure on the system size. The error bar of the most efficient FCIQMC algorithm will decay fastest as a function of computer time. We then draw conclusions about the applicability of the FCIQMC method. Finally we describe an implementation of FCIQMC on a novel data flow computer architecture. In our implementation we made a modification to the FCIQMC algorithm to fit the data flow paradigm. We investigate the efficiency of the modified FCIQMC algorithm.
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Spencer, Paul E. "Continuous-time quantum Monte Carlo studies of lattice polarons". Thesis, Loughborough University, 2000. https://dspace.lboro.ac.uk/2134/33799.
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The polaron problem is studied, on an infinite lattice, using the continuous-time path-integral quantum Monte Carlo scheme The method is based on the Feynman technique to analytically integrate out the phonon degrees of freedom. The transformed problem is that of a single electron with retarded self-interaction in imaginary time. The Metropolis algorithm is used to sample an ensemble of electron trajectories with twisted (rather than periodic) boundary conditions in imaginary time, which allows dynamic properties of the system to by measured directly. The method is numerically "exact", in the sense that there are no systematic errors due to finite system size, trotter decomposition or finite temperature The implementation of the algorithm in continuous imaginary time dramatically increases computational efficiency compared with the traditional discrete imaginary time algorithms.
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Makivic, Miloje S. Cross Michael Clifford Cross Michael Clifford. "Monte Carlo studies of two dimensional quantum spin systems /". Diss., Pasadena, Calif. : California Institute of Technology, 1991. http://resolver.caltech.edu/CaltechETD:etd-07202007-094134.
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Chow, Fung-kiu. "Quantum statistical mechanics a Monte Carlo study of clusters /". Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22424799.
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Cho, Hyung Min. "A full-dimensional quantum Monte Carlo study of H5O2+". Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1085048780.
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Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains xii, 88 p.; also includes graphics (some col.). Includes bibliographical references (p. 83-88). Available online via OhioLINK's ETD Center
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Galek, Peter Tadeusz A. "Atomic and molecular electronic structure and quantum chemical calculations with quantum Monte Carlo". Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614146.
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Osychenko, Oleg N. "Monte Carlo study of quantum phase transitions at zero temperature". Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/123715.
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The Thesis is devoted to simulations of quantum phase transitions by means of Quantum Monte Carlo techniques.
Quantum phase transition is a transition between phases at zero or low enough temperature, where quantum effects play an important role. The recent advances in the field of ultracold atom manipulation and optical lattices allowed to produce the systems with unique properties. This opened a perspective to observe quantum phase transitions in many-body systems with non-trivial interparticle interactions in a wide range of the system's characteristic physical parameters and geometries.
First, we develop the explicit expressions for the Ewald sums in systems with an interaction potential of a generic 1/r^k type, and in 3D, 2D and 1D geometry. These generalizations can be useful in simulating systems with important interaction potentials as the dipole-dipole, van der Waals interaction, etc. In this Thesis we give the functional forms for the terms of the Ewald sums, ready for implementation in a code. The derivation and the functional form of the results differ in the cases of short-ranged, long-ranged and "marginal" forces, and for a jellium model. It is argued that in the case of some short-range potentials the Ewald method can be advantageous with respect to a direct summation due to a faster convergence rate. We also give a discussion of the convergence properties of a quasi-neutral Coulomb system.
We have obtained the zero-temperature phase diagram of bosons interacting through Yukawa forces. We have used a diffusion Monte Carlo simulation starting from a good approximation to the optimal variational ground-state wave function obtained by solving the corresponding Euler-Lagrange hypernetted chain equations. The phase diagram shows that any fermionic mixture of pure elements will always be seen in gaseous form, as the mass ratios required for crystallization of weakly bound fermionic molecules are far beyond the ones that can be achieved in nature. We investigate an alternative mechanism based on the confinement of one of the species to a deep optical lattice which increases its effective mass. The resulting mass ratio of the mixture created in this way can then be tuned at will and could be used to check experimentally the predicted phase diagram both in the gas and crystal (superlattice) phases.
We performed a QMC study of the system, comrised of Rydberg atoms. The applied QMC techniques allowed to parametrize a model with isotropic van der Waals interactions into a universal phase diagram. We have characterized the phase diagram of Rydberg atoms by considering a model of bosons with repulsive van der Waals 1/r^6 interaction, and determined solidification and Bose-Einstein condensation conditions. Relaxation mechanisms other than thermal motion should be considered if one considers Rydberg systems on timescales of several tenths of microseconds. We have also studied the excitation spectrum within the approximation of a classical harmonic crystal. We also discuss that interactions between Rydberg excitations open a possibility of new supersolid scenarios.
In the last Chapter of the Thesis I present a study of the system of para-hydrogen atoms at low temperatures below the point of crystallization by means of QMC methods. The zero-temperature simulation was performed in order to investigate the properties of a metastable liquid phase and to find the fraction of the Bose-Einstein condensate in the relevant range of densities. The methods of choice for the zero-temperature simulations of the para-H2 system were VMC and DMC techniques. The results of the zero-temperature simulations suggest that the metastable liquid para-hydrogen is a strongly correlated liquid, which again serves as an evidence of high instability of this hypothetical system. The calculation of the Bose-Einstein condensate shows that the condensate fraction is substantially lower than in the liquid helium He4.Los avances recientes en manipulación de átomos ultrafrios y retículos ópticos abrieron la posibilidad de observar las transiciones de fase en sistemas de muchos cuerpos con las interacciones interparticulares no triviales para un amplio rango de los parámetros físicos característicos y geometrías del sistema. En principio desarrollamos las expresiones explicitas para las sumas de Ewald en el caso del potencial de interacción genérico 1/r^k, y en las geometrías arbitrarias: 3D, 2D y 1D. Dichas generalizaciones pueden ser útiles para simular sistemas con los potenciales importantes como dipolo-dipolo, interacción de van der Waals, etc. En la Tesis presentamos las formas funcionales para los términos de las sumas de Ewald, listas para la implementación actual. La derivación y las formas funcionales cambian en función de la potencial de corto, largo o alcance "marginal", y en particular para el modelo de jellium. Argüimos que en el caso del potencial de corto alcance el método de Ewald puede ser ventajoso respecto a la sumatorio directo gracias a la convergencia más rápida. También presentamos la discusión sobre las propiedades de convergencia del sistema de Coulomb сuasi-neutro. Hemos obtenido el diagrama de fase a temperatura cero de los bosones interactuando mediante a las fuerzas de Yukawa. Hemos usado la simulación de Monte Carlo difusivo empezando de una buena aproximación a la función de onda óptima del estado de base obtenida a través de la solución de las ecuaciones de Euler-Lagrange del método HNC. El diagrama de fase demuestra que la mezcla fermiónica de los elementos puros siempre aparece en la forma gaseosa, como los parametros requeridos para la cristalización de estas moléculas fermiónicas están fuera de lo que puede ser visto en la naturaleza. Investigamos el mecanismo alternativo basado en el confinamiento de una de las especies en el retículo óptico, que aumenta su masa efectiva. El cociente de masas de la mezcla creada de esta manera puede ser ajustada arbitrariamente y usada para comprobar el diagrama de fase predicha en el estudio tanto en fase liquida como en la cristalina. Hemos hecho el estudio QMC del sistema de los átomos de Rydberg. Las técnicas de Monte Carlo cuánticas aplicadas nos permitieron parametrizar el modelo mediante la interacción de van der Waals isotrópica y así obtener el diagrama de fase universal. Caracterizamos el diagrama de fase de los átomos de Rydberg considerando el modelo de bosones con la interacción repulsiva 1/r^6, y determinamos las condiciones de solidificación y condensación de Bose-Einstein. Los mecanismos de relajación aparte del movimiento térmico deben de ser tenidos en cuenta a escala de tiempo de decenas de microsegundos. Estudiamos también el espectro de excitaciones dentro de la aproximación de cristal clásico harmónico. Finalmente, discutimos que las interacciones entre las excitaciones de Rydberg abren la posibilidad de los escenarios nuevos del supersólido.
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Brualla, Barberà Llorenç. "Path integral Monte Carlo. Algorithms and applications to quantum fluids". Doctoral thesis, Universitat Politècnica de Catalunya, 2002. http://hdl.handle.net/10803/6577.
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Path integral Monte Carlo (PIMC) is a method suitable for quantum liquid simulations at finite temperature. We present in this thesis a study of PIMC dealing with the theory and algorithms related to it, and then two applications of PIMC to current research problems of quantum fluids in the Bolzmann regime. The first part encompasses a study of the different ingredients of a PIMC code: action, sampling and physical property estimators. Particular attention has been paid to Li-Broughton's higher order approximation to the action. Regarding sampling, several collective movement methods have been derived, including the bisection algorithm, that has been thoroughly tested. We also include a study of estimators for different physical properties, such as, the energy (through the thermodynamic and virial estimators), the pair distribution function, the structure factor, and the momentum distribution.
In relation to the momentum distribution, we have developed a novel algorithm for its estimation, the trail method. It surmounts some of the problems exposed by previous approaches, such as the open chain method or McMillan's algorithm.
The Richardson extrapolation used within PIMC simulations, is another contribution of this thesis. Up until now, this extrapolation has not been used in this context. We present studies of the energy dependence on the number of "beads", along with the betterment provide by the Richardson extrapolation.
Inasmuch as our goal is to perform research of quantum liquids at finite temperature, we have produced a library of codes, written from scratch, that implement most of the features theoretically developed. The most elaborated parts of these codes are included in some of the appendixes.
The second part shows two different applications of the algorithms coded. We present results of a PIMC calculation of the momentum distribution of Ne and normal 4He at low temperatures. In the range of temperatures analysed, exchanges can be disregarded and both systems are considered Boltzmann quantum liquids. Their quantum character is well reflected in their momentum distributions witch show clear departures from the classical limit. The PIMC momentum distributions which show clear departures from the classical limit. The PIMC momentum distributions are sampled using the trail method. Kinetic energies of both systems, as a function of temperature and at a fixed density, are also reported.
Finally, the solid-liquid neon phase transition along the 35 K isotherm has been characterized.While thermodynamic properties of the solid phase are well known the behaviour of some properties, such as the energy or the dessity, during the trasition presen6 some uncertainties For example, experimental data for the place diagram, which determines solid and liquid boundaries, present sizeable differences. The temperature chosen is high enough so that Bose or Fermi statistics corrections are small, although the system is strongly quantum mechanical. The results obtained show a discontinuity in the kinetic energy during the transition.
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James, Alan John. "Solving the many electron problem with quantum Monte-Carlo methods". Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309224.
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Sémon, Patrick. "Continuous-Time Quantum Monte Carlo Impurity Solvers: Improvements and Applications". Thèse, Université de Sherbrooke, 2014. http://savoirs.usherbrooke.ca/handle/11143/5289.
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Abstract: Originally designed for the study of strong electronic correlations in model Hamiltonians, dynamical mean field theory (DMFT) has become, in combination with density functional theory (DFT), a powerful tool for ab initio simulations of real materials. At the heart of DMFT lies the solution of a quantum impurity problem. While only the continuous-time quantum Monte Carlo (CT-QMC) impurity solvers yield (statistically) exact solutions of a general impurity problem, they are quite complex and computationally expensive. Hence, in this thesis we are interested in improving the CT-QMC impurity solvers. After a short introduction to DMFT and its cluster extensions, we begin by reviewing two of the CT-QMC impurity solvers, the interaction expansion or “Rubtsov” solver (CT- INT) and the hybridization expansion solver (CT-HYB). Focussing on the latter, which is the algorithm of choice within real material simulations, we then show how to reduce a sign problem, allowing us to address the unusual criticality found in layered organic superconductors. With high-T c superconductivity as example, we further discuss how to ensure ergodicity of the CT-HYB solver in the context of broken symmetries. Finally, algorithmic optimizations of CT-HYB are presented and combined, leading to speedups of up to 500 within the context of real material simulations. // Résumé: Initialement conçue pour traiter les fortes corrélations électroniques dans des hamiltoniens modèles, la théorie du champ moyen dynamique (DMFT) est devenue, en combinaison avec la théorie de la densité fonctionnelle (DFT), un outil puissant pour la simulation de matériaux réels. Au cœur de la DMFT se trouve la solution d'un modèle d'impureté quantique. Seulement les solutionneurs d'impureté Monte Carlo en temps continu (CT-QMC) donnent des solutions exactes. En même temps, ces solutionneurs sont plutôt complexes et gourmands en temps de calcul. Le but de cette thèse est donc d'améliorer les solutionneurs d'impureté CT-QMC. Après une courte introduction à la DMFT et à ses extensions pour les amas, on commence par une revue de deux des solutionneurs CT-QMC, celui en développement d'interaction ou de "Rubtsov" (CT-INT) et celui en développement d'hybridation (CT-HYB). Mettant l'accent sur le dernier, qui est l'algorithme de choix dans le cadre des matériaux réels, on montre alors comment réduire un problème de signe, nous permettant ainsi de traiter la criticalité inhabituelle des organiques en couche. Avec la supraconductivité à haute température critique comme exemple, on discute ensuite comment assurer l'ergodicité du solutionneur CT-HYB dans le cadre des symétries brisées. Finalement, des optimisations algorithmiques sont présentées et combinées, amenant à des accélérations allant jusqu'à un facteur de 500 dans le contexte des matériaux réels.
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Hoare, David. "Monte Carlo simulations of electron transport in quantum well heterostructures". Thesis, Durham University, 1993. http://etheses.dur.ac.uk/5557/.
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The parallel transport of electrons in pseudomorphic In(_z)Ga(_1-x)As/GaAs quantum wells is influenced by the degree of spacial confinement and by the effect of the indium concentration which determines, the amount of alloy scattering, the subband structure, and material parameters. The indium content changes the bandstructure and material parameters through both direct compositional and strain effects. We use the single particle and ensemble methods of Monte-Carlo simulation to investigate how the above phenomena influence the transport properties of electrons in In(_x)Ga(_1-x)As/GaAs quantum wells. To understand the effects of alloying and strain on the electron transport properties we first consider electrons in bulk In(_x)Ga(_1-x)As/GaAs. Alloying and strain are considered in artificial systems were the effect(s) of these factors on electron transport may be isolated. For a range of indium compositions, we consider independently the effects of alloying (with and without alloy scattering) and strain on the bandstructure and material parameters and, in turn, their effects on the electron transport properties. We show that increasing the indium concentration generally improves the carrier low field mobility and peak velocity of unstrained materials but has a detrimental effect on the saturation velocity. Strain reduces the low field mobility and peak velocity but gives a slightly higher saturation velocity when compared to GaAs, and the unstrained system. Comparison of transient and steady state transport phenomena is made for strained In(_0.15)Ga(_0.085)As/GaAs quantum well structures, at fields high enough for real- and reciprocal-space transfer to occur. An artificial case, called the unstrained system, where the strain effects on the bandstructure and material parameters are neglected is also considered. Differences between the strained and unstrained well results are small and mainly transient. At steady state, most of the electrons for almost all fields reside in unbound states. The strained and unstrained systems show higher low field mobilities when compared to bulk GaAs. Lattice vibrations are also affected by heterostructures and we have made a study of the effects on the low field transport of electrons in a 70Å Al(_0.3)Ga(_0.7)As/GaAs quantum well when the polar optical phonon modes which interact with the electrons are described by three phonon models which describe the lattice vibrations of the heterostructure; the Hydrodynamic Model (EDM), the Dielectric Continuum Model (DCM), and the Bulk Phonon Approximation (BPA). We show that the BPA and EDM predict similar transport effects and are in good agreement with experimental results. We conclude that, at present, the BPA is an adequate model to describe the phonon modes in heterostructure quantum wells for use in transport calculations.
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Winklbauer, Stephen Peter. "Semi-classical and quantum Monte Carlo simulations in optical lattices". Thesis, University College London (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.404893.
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López, Ríos Pablo. "Backflow and pairing wave function for quantum Monte Carlo methods". Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/288882.
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Quantum Monte Carlo (QMC) methods are a class of stochastic techniques that can be used to compute the properties of electronic systems accurately from first principles. This thesis is mainly concerned with the development of trial wave functions for QMC. An extension of the backflow transformation to inhomogeneous electronic systems is presented and applied to atoms, molecules and extended systems. The backflow transformation I have developed typically retrieves an additional 50% of the remaining correlation energy at the variational Monte Carlo level, and 30% at the diffusion Monte Carlo level; the number of parameters required to achieve a given fraction of the correlation energy does not appear to increase with system size. The expense incurred by the use of backflow transformations is investigated, and it is found to scale favourably with system size. Additionally, I propose a single wave function form for studying the electron-hole system which includes pairing effects and is capable of describing all of the relevant phases of this system. The effectiveness of this general wave function is demonstrated by applying it to a particular transition between two phases of the symmetric electron-hole bilayer, and it is found that using a single wave function form gives a more accurate physical description of the system than using a different wave function to describe each phase. Both of these developments are new, and they provide a powerful set of tools for designing accurate wave functions. Backflow transformations are particularly important for systems with repulsive interactions, while pairing wave functions are important for attractive interactions. It is possible to combine backflow and pairing to further increase the accuracy of the wave function. The wave function technology that I have developed should therefore be useful across a very wide range of problems.
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Thom, Alexander James William. "Towards a quantum Monte Carlo approach based on path resummations". Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613116.
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Cikojević, Viktor. "Ab-initio quantum Monte Carlo study of ultracold atomic mixtures". Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/672119.
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The properties of mixtures of Bose-Einstein condensates at T=0 have been investigated using quantum Monte Carlo (QMC) methods and Density Functional Theory (DFT) with the aim of understanding physics beyond the mean-field theory in Bose-Bose mixtures. In particular, quantum liquid droplets with attractive intraspecies and repulsive interspecies attraction were studied, for which we observed significant contributions beyond Lee Huang Yang (LHY) theory that affect the energy, saturation density, and surface tension. The critical atom number in droplets in free space for total number of atoms N between N=30 and N=2000 was obtained. Results of the surface tension for three values of the attractive interspecies interactions are presented. For a homogeneous system, extensive calculations of the equations of state were performed and we report the influence of finite-range effects in beyond-Bogoliubov theory. In systems interacting with a small (large) effective range, we observe repulsive (attractive) beyond-LHY contributions to the energy. For the droplets in a mixture of 39K atoms, which were observed experimentally for the first time, the calculations of equations of state were performed. Combining QMC-built functionals with DFT, the discrepancy in the estimation of critical atom number between the mean-field theory and experimental results was explained by the proper inclusion of the effective range in inter-particle interaction models. The influence of finite-range effects on breathing and quadrupole modes in 39K quantum droplets was investigated. We predicted a significant deviation in the excitation frequencies when entering a more correlated regime. Finally, the phase diagram of repulsive Bose-Bose mixtures in a spherical harmonic trap using Quantum Monte Carlo calculations was studied. Density profiles were obtained reported and we found the occurrence of three phases: separation of condensates in two blobs, fully mixed and shell-separated phase. A comparison with the Gross-Pitaevskii solutions showed a large deviation in the regime of large mass imbalance and strong interactions. We showed the universality in the density profiles with respect to the s-wave scattering length and found numerical evidence for Gross-Pitaevskii scaling present beyond the regime of applicability of Gross-Pitaevskii equations.Hemos investigado las propiedades de las mezclas de condensados de Bose-Einstein en el límite de temperatura cero. Para ello hemos usado métodos cuánticos de Monte Carlo (QMC) y la teoría del funcional de la densidad (DFT) con el objetivo de comprender la física más allá de la teoría del campo medio en las mezclas bosónicas. En particular, se estudiaron las gotas de líquido cuántico originadas con interacciones atractivas entre especies distinats y repulsivas entre especies iguales. Observamos contribuciones significativas más allá de la teoría de Lee Huang Yang (LHY) que afectan a la energía, la densidad de saturación y la tensión superficial. Calculamos el número crítico de átomos en gotitas en el espacio libre para un número total de átomos N entre N = 30 y N = 2000. Obtuvimos resultados de la tensión superficial para tres valores de las interacciones atractivas entre especies. Para un sistema homogéneo, se realizaron cálculos extensos de las ecuaciones de estado y reportamos la influencia de los efectos de rango finito en la teoría, más allá de Bogoliubov. En sistemas que interactúan con un rango efectivo pequeño (grande), observamos contribuciones repulsivas (atractivas) a la energia más allá de LHY. Para las gotitas en una mezcla de 39K átomos, que se observaron experimentalmente por primera vez en ICFO, se realizaron los cálculos de ecuaciones de estado. Combinando funciones obtenidas de QMC con DFT, explicamos la discrepancia en la estimación del número crítico de átomos, entre la teoría de campo medio y los resultados experimentales, mediante la inclusión adecuada del rango efectivo en los modelos de interacción entre partículas. Se investigó la influencia de los efectos de rango finito en los modos monopolar y cuadrupolar en gotas cuánticas de 39K. Predijimos una desviación significativa en las frecuencias de excitación al entrar en un régimen más correlacionado. Finalmente, se estudió el diagrama de fase de mezclas bosóncas repulsivas en una trampa armónica esférica utilizando cálculos de Quantum Monte Carlo. Se obtuvieron los perfiles de densidad y se probó la existencia de tres fases: separación de condensados en dos lóbulos, una fase completamente mezclada y una fase separada con capas esféricas. Una comparación con las soluciones de Gross-Pitaevskii mostró una gran desviación en el régimen de gran desequilibrio de masas e interacciones fuertes. Finalmente, mostramos la presencia de universalidad en los perfiles de densidad, con respecto a la longitud de dispersión en onda S, y encontramos evidencia numérica del factor de escala de Gross-Pitaevskii más allá del régimen de aplicabilidad de las propias ecuaciones de Gross-Pitaevskii.
Ultrahladne atomske mješavine istražene ab-initio kvantnom Monte Carlo metodom. Svojstva smjesa Bose-Einsteinovih kondenzata pri T = 0 istražena su korištenjem metoda kvantnog Monte Carla (QMC) i teorije funkcionala gustoće (DFT) s ciljem proučavanja fizike izvan teorije srednjeg polja u bozonskim mješavinama. Proučili smo kvantne kapljice s jednakim i odbojnim interakcijama između atoma istovrsne komponente te privlačnim interakcijama atoma različitih komponenti u interakciji i opazili smo značajne doprinose povrh Lee Huang Yang (LHY) teorije koji utječu na energiju, saturacijsku gustoću i površinsku napetost. Odredili smo kritični broj atoma za kapljice u slobodnom prostoru za broj atoma u kapljici N između N = 30 i N = 2000. Izračunali smo površinsku napetost za tri vrijednosti privlačnih međuatomskih interakcija. Izvršili smo opsežne proračune jednadžbi stanja iznimno rijetke tekućine bozonske mješavine i uočili utjecaj efekata konačnog dosega koji nije predviđen Bogoliubovljevom teorijom. U sustavima koji interagiraju s malim (velikim) efektivnim dosegom, opaženi su odbojni (privlačni) doprinosi koje ne predviđa LHY teorija. Izračunali smo jednadžbe stanja za kapljice bozonskih mješavina koje su po prvi put eksperimentalno uočene u smjesi 39K atoma. Kombinirajući funkcionale gustoće izgrađene pomoću kvantnog Monte Carla s DFT-om, neslaganje u procjeni kritičnog broja atoma između teorije srednjeg polja i eksperimentalnih rezultata je objašnjeno preko pravilnog uključivanja efektivnog dosega u modele međudjelovanja čestica. Istražen je utjecaj efektivnog dosega na pobuđenja kapljice 39K, i to na mod disanja i kvadrupolni mod. Dobiveni rezultati prikazuju značajno odstupanje frekvencija pobude pri ulasku u korelirani režim. Detaljno smo proučili fazni dijagram odbojnih Bose-Bose mješavina u sfernoj harmonijskoj zamci koristeći kvantne Monte Carlo račune. Dobiveni su profili gustoće koji pokazuju pojavu tri faze: separacija kondenzata u dvije nakupine, potpuno miješanje i separacije u obliku ljuske. Usporedba s riješenjima Gross-Pitaevskii jednadžbi pokazuje veliko odstupanje u režimu velike masene neravnoteže i jakih interakcija. Pokazali smo univerzalnost profila gustoće s obzirom na s-valnu duljinu raspršenja te postojanje Gross-Pitaevskii skaliranja prisutnog izvan dosega primjenjivosti Gross-Pitaevskii jednadžbi.
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Dagrada, Mario. "Improved quantum Monte Carlo simulations : from open to extended systems". Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066349/document.
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Dans cette thèse nous présentons des progrès algorithmiques ainsi que plusieurs applications des méthodes de Monte Carlo quantique (QMC) pour simulations à partir des premiers principes. Les améliorations que nous proposons permettent d'étudier par QMC des systèmes de plus grosse taille voire périodiques, avec l'ambition de faire du QMC une alternative valable à la théorie de la fonctionnelle de la densité (DFT). Tous les résultats ont été obtenus par le logiciel TurboRVB. D'abord, nous présentons une implémentation du QMC basée sur la fonction d'onde Jastrow-Geminale qui combine une grande flexibilité avec un traitement précis des corrélations électroniques. On a appliqué une technique originale de plongement pour réduire la taille de la base atomique à la molécule d'eau ainsi qu'à un modèle simplifié du transfert de protons (TP) dans l'eau. Nos résultats ouvrent la voie à l'étude des phénomènes microscopiques tels que le TP directement par QMC. Ensuite, on a amélioré notre méthode afin de simuler les solides cristallins. Grâce à une nouvelle procédure pour choisir de manière appropriée les conditions aux limites, nous avons pu réduire les erreurs de taille finie qui affectent les simulations QMC des solides. Sur la base des techniques développées, nous étudions enfin le supraconducteur FeSe. Le QMC fournit le meilleur résultat concernant sa structure cristalline; via une étude systématique du paysage énergétique à différentes configurations magnétiques, nous montrons un lien fort entre la structure, le magnétisme et les mouvements de charge dans ce matériau, prélude à une compréhension quantitative de la supraconductivité à haute température des premiers principesIn this thesis we present algorithmic progresses as well as applications of continuum quantum Monte Carlo (QMC) methods for electronic structure calculations by first principles. The improvements we propose allow to tackle much larger molecular as well as extended systems by QMC, with the ultimate goal of making QMC a valid alternative to density functional theory (DFT). All results have been obtained with the TurboRVB software, which we contributed to develop. At first, we present a QMC framework based on the Jastrow-Geminal wavefunction which combines great flexibility with a compact analytical form, while providing at the same time an accurate treatment of electron correlations. We apply an original atomic embedding scheme for reducing the basis set size to the water molecule and to a simple model of proton transfer (PT) in aqueous systems. Our results pave the way to the study of microscopic phenomena such as PT directly by QMC. Afterwards, we extend our QMC framework in order to simulate crystalline solids. We propose a novel procedure to find special values of the boundary conditions which allow to greatly reduce the finite-size errors affecting solid state QMC simulations. Using the techniques previously developed, we study the iron-based superconductor FeSe. We show that QMC provides the best crystal structure predictions on this compound; by means of a systematic study of the energy landscape at different magnetic orderings, we show a strong link between structural, magnetic and charge degrees of freedom in FeSe. Our results represent an important step towards a quantitative understanding of high-temperature superconductivity by first-principles
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Andreoli, Lorenzo. "A Quantum Monte Carlo approach to dark matter-nuclei interaction". Doctoral thesis, Università degli studi di Trento, 2019. https://hdl.handle.net/11572/369194.
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Using quantum Monte Carlo Methods, we compute the differential cross sections for elastic scattering of dark matter (DM) particles off light nuclei, up to $A=6$
(d, $^3$H, $^3$He, $^4$He, and $^6$Li).
DM-nucleon one- and two-body currents are obtained to next-to-leading order in chiral effective theory, and they are derived from a DM-quark and DM-gluon effective interaction.
The nuclear ground states wave functions are obtained from a phenomenological nuclear Hamiltonian, composed of the Argonne $v_{18}$ two-body interaction and the three-body Urbana IX. In this framework, we study the impact of one- and two-body currents and discuss the size of nuclear uncertainties.
This work evaluates for the first time two-body effects in $A=4,6$ systems and provides the nuclear structure input
that can be used to assess the sensitivity of future experimental searches of (light) dark matter,
especially relevant for possible experimental targets such as $^3$He and $^4$He.
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Andreoli, Lorenzo. "A Quantum Monte Carlo approach to dark matter-nuclei interaction". Doctoral thesis, University of Trento, 2019. http://eprints-phd.biblio.unitn.it/3770/2/Disclaiemr_Andreoli.pdf.
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Using quantum Monte Carlo Methods, we compute the differential cross sections for elastic scattering of dark matter (DM) particles off light nuclei, up to $A=6$
(d, $^3$H, $^3$He, $^4$He, and $^6$Li).
DM-nucleon one- and two-body currents are obtained to next-to-leading order in chiral effective theory, and they are derived from a DM-quark and DM-gluon effective interaction.
The nuclear ground states wave functions are obtained from a phenomenological nuclear Hamiltonian, composed of the Argonne $v_{18}$ two-body interaction and the three-body Urbana IX. In this framework, we study the impact of one- and two-body currents and discuss the size of nuclear uncertainties.
This work evaluates for the first time two-body effects in $A=4,6$ systems and provides the nuclear structure input
that can be used to assess the sensitivity of future experimental searches of (light) dark matter,
especially relevant for possible experimental targets such as $^3$He and $^4$He.
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Luo, Ye. "Ab initio molecular dynamics of water by quantum Monte Carlo". Doctoral thesis, SISSA, 2014. http://hdl.handle.net/20.500.11767/3896.
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The chapter 2, we deal with the challenge b). It focuses on the variational
Monte Carlo (VMC) and the wavefunction optimization methods based on
VMC. The performance of different methods are displayed through the op-
timization of the Jastrow factor in our test case Beryllium dimer and the
efficiency is improving surprisingly during the evolution of these methods.
In chapter 3, we focus on the challenge a). It describes the wavefunc-
tion ansatz used by our simulation. In this thesis, we introduce the atomic
hybrid orbitals which significantly increase the compactness of our wavefunc-
tion without hurting accuracy. This chapter also explain how to optimize
the determinant in a way that the number of variational parameters scales
only linearly with the system size. This further helps the efficiency of the
wavefunction optimization.
In chapters 4 and 5, the issue c) is explained in detail. In chapter 4,
a second order Langevin dynamics (SLD) scheme is devised particularly for
QMC and this thesis improves this scheme by developing a better integration
method. Here, we also highlight the remarkable power of the force covari-
ance matrix which can be defined only in QMC and is capable of accelerating
the slow modes of a dynamics. In chapter 5, this SLD for QMC is validated
through intensive benchmarking on the calculation of the vibrational frequen-
cies of water and other small molecules. It is shown that many systematic
biases in our MD scheme and QMC evaluation can be controlled so that we
are confident to push forward this ab initio molecular dynamics for applica-
tions on large systems.
Finally in chapter 6, we perform the simulation of liquid water with all the
preparation done in the previous chapters. The results are encouraging since
we’ve closed the discrepancy of the peak positions of RDFs between experi-
ments and ab initio simulations. The power of QMC is also demonstrated by
the fact that the shapes of our RDFs are much less structured than previous
DFT-based ab initio simulations even if the two water molecule interaction is
dealt with the same level of accuracy as the DFT/BLYP calculation. In this
chapter, we have also studied the features of hydrogen bonds in our simulation
of liquid water. All our results indicate that it is important to consider the
quantum nature of the ions for a faithful description of liquid water. This will
be left for future studies, possible in principle even within the QMC approach.
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Ardekani, Armin. "Monte Carlo studies of two dimensional field theories /". Title page, table of contents and introduction only, 1998. http://web4.library.adelaide.edu.au/theses/09PH/09pha676.pdf.
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Ferré, Porta Guillem. "A Monte Carlo approach to statics and dynamics of quantum fluids". Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/459067.
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The main objective of the thesis is to study static and/or dynamic properties of a set of quantum fluids by means of quantum Monte Carlo techniques, mainly using the path integral formalism to obtain results both at zero temperature and finite temperature. First, we present briefly some of the more important quantum Monte Carlo methods, and introduce the Path Integral Monte Carlo (PIMC) method, which has been used during all this thesis, as well as the Path Integral Ground State (PIGS), which is an extension of the first at ground state. After introducing the basic formalism, we comment on the approximations needed and provide a comparison between different actions. We also comment on parallelization schemes and advanced sampling techniques.
The first results shown in this thesis are for the phase diagram of a one-dimensional Coulomb gas, which have been obtained using the PIMC method. The phase diagram have been constructed mainly by calculating energetic and structural properties. The obtained results extend previous knowledge of different phases in the one-dimensional Coulomb gas at zero temperature. Our results show the existence of a quantum Wigner crystal regime and a Ideal Fermi gas regime at low temperatures. As temperature increases, we reach a classic Wigner crystal regime and a classical gas.
In the following chapter we show the results of a quasi-one-dimensional para-H2. The aim of this work is to see how the quasi-one-dimensionality affects the Luttinger parameter when comparing it with the pure one-dimensional case. This is done at zero temperature using PIGS. As para-hydrogen is an important candidate to superfluidity, the main idea behind study a quasi-one-dimensional system is to reduce dimensionality in order to soften intermolecular interaction. For that, we try different external potentials to control the opening of the system in two dimensions. Despite an increase in the Luttinger parameter in the various quasi-one-dimensional cases, it still does not reach the values displaying superfluidity.
The next work shown in the thesis is our extensive study of the dynamic structure factor for the 4He. Using Path Integral Monte Carlo, we compute the intermediate scattering function at different temperatures and perform an inversion in order to gain access at the dynamics of the system. Despite the ill-posed problem of this inversion, we obtain results in a qualitative agreement with the experiments and prove that our method of inversion, despite having to yield with inversion problems achieves to obtain better numerical results for 4He at finite temperature than the ones previously reported. In this sense, we provide comparisons with the Maximum Entropy method and with experimental results. The study at different temperatures shows us the dissappearance of the roton peak when we cross T=2.17K from the superfluid regime to the normal fluid. We also observe a kink in the momentum distribution at the superfluid regime that dissappears at higher temperatures, for which does not exist an explanation in the theory.
In the final chapter of the thesis we provide a method to sample complex-time correlation functions whose aim is to obtain better dynamic structure factor functions than the ones obtained via pure imaginary-time correlation functions. This model has already been tested for single-particle systems. Our aim is to test it for multi-particle systems, and to see if we can still recover good results at a reasonable high complex-time when the number of particles is closer to the typical simulation values of real systems. We tested it with particles interacting with an harmonic potential. Despite an increased variance compared with the one-particle case, we obtain good results that allow us to obtain the dynamic structure factor. Comparing the results with ones obtained at pure-imaginary time, we show how the complex-time inversion is superior and provides results closer to the exact ones.L'objectiu principal d'aquesta tesi es l'estudi de propietats estàtiques i dinàmiques de diferents fluids quàntics utilitzant tècniques de Monte Carlo quàntiques, principalment emprant el formalisme de path integrals per obtenir resultats tan a temperatura zero com a temperatura finita. Primer de tot, presentem els mètodes de Monte Carlo quàntics més importants, i introduïm el mètode de Path Integral Monte Carlo (PIMC), que fem servir al llarg de tota la tesi, i el mètode de Path Integral Ground State (PIGS), que es una extensió del primer però a temperatura zero. Després d'introduir el formalisme bàsic, comentem les diferents aproximacions necessàries i aportem una comparació entre elles. També expliquem un possible mètode de paral·lelització i tècniques de mostreig avançat. Els primers resultats que mostrem en aquesta tesi son pel diagrama de fases d'un gas de Coulomb unidimensional, que hem obtingut emprant PIMC. Hem construït el diagrama de fases mitjançant el càlcul de propietats energètiques i estructurals. Els nostres resultats amplien estudis previs que s'havien realitzat pel mateix sistema a temperatura zero. Els nostres resultats mostren l'existència d'un règim de cristall de Wigner quàntic i un d'un gas de Fermi ideal a temperatures baixes. Incrementant la temperatura obtenim un cristall de Wigner clàssic i un gas clàssic. En el següent capítol ensenyem els resultats per un sistema quasi-unidimensional de parahidrogen. L'objectiu d'aquest estudi es veure si la quasi-unidimensionalitat afecta al paràmetre de Luttinger quan el comparem pel cas purament unidimensional. Això ho fem a temperatura zero utilitzant PIGS. Sent el parahidrogen un fort candidat a ser superfluid, la idea principal es veure si reduint la dimensionalitat del sistema podem alleugerir suficient la interacció intermolecular. Per fer-ho, provem diferents potencials externs per controlar l'obertura del sistema en dues de les dimensions. Tot i l'increment del paràmetre de Luttinger respecte al cas unidimensional, aquest no arriba als valors esperats per mostrar superfluïdesa. El següents resultats són del nostre estudi sobre el factor d'estructura dinàmic per 4He. Utilitzant PIMC, calculem la funció de dispersió a diferents temperatures i fem una inversió per tal d'accedir a les propietats dinàmiques del sistema. Tot i la naturalesa de problema mal posat d'aquesta inversió, obtenim resultats qualitativament bons en comparació amb els experimentals, i provem que el nostre mètode d'inversió obté resultats superiors per 4He a temperatura finita que els obtinguts prèviament utilitzant altres mètodes. En aquest sentit, aportem una comparació amb el mètode de màxima entropia i amb resultats experimentals. L'estudi a diferents temperatures ens deixa veure la desaparició del pic del rotó quan creuem T=2.17K des de el règim superfluid al fluid normal. També observem una curvatura estranya en la distribució de moments en el règim de superfluïdesa que desapareix a temperatures més elevades, i pel qual no existeix cap explicació teòrica. Finalment, mostrem un mètode per calcular funcions de correlació en temps complex, l'objectiu del qual es obtenir factors d'estructura dinàmic superiors als obtinguts en temps purament imaginari. Aquest model ha sigut provat amb èxit en sistemes d'una sola partícula. El nostre objectiu es veure si obtenim resultats bons en sistemes amb més partícules, i si el temps complex màxim al que podem accedir no es redueix amb aquest increment. Tot i l'increment en la variança, obtenim bons resultats pel factor dinàmic i, comparant-los amb els obtinguts amb temps imaginari, podem veure com el temps complex ofereix resultats més pròxims als exactes.
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Bombín, Escudero Raúl. "Ultracold Bose and Fermi dipolar gases : a quantum Monte Carlo study". Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/668241.
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The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the the Schrödinger equation. In the present study we employ different Monte Carlo methods that allow to find numerical solutions to it by employing a set of stochastic techniques. The simplest one that we introduce corresponds to the Variational Monte Carlo (VMC) method, that despite its simplicity, allows to obtain variational solutions to the many-body problem. A more accurate description is provided by Diffusion Monte Carlo (DMC), that provides exact solutions for the ground state of the system when dealing with bosons. We continue presenting two methods that rely on the Feynman's path integral formalism of quantum mechanics: Path Integral Monte Carlo (PIMC) and Path Integral Ground State (PIGS), that provide exact solutions for the bosonic problem at finite and zero temperature respectively. In order to work with fermionic systems, as we do in chapter 4 of this thesis, the DMC algorithm has to be modified with the Fixed-Node (FN) approximation, what alows to avoid the sign problem. Doing so, the results obtained with DMC correspond to variational upper bounds to the energy.
In chapter 3 we study the superfluid properties of a system of dipolar bosons that are fully polarized and in which the atoms are restricted to move in the plane. We also consider that all the dipolar moments form a certain tilting angle with the axis perpendicular to the plane, what allows to introduce anisotropy in the system. The phase diagram at zero temperature of this system reveals the existence of three different phases: gas, stripe and solid. Here we focus on the characterization of the superfluid properties across that phase diagram. Our calculations allow to address the question of whether the stripe phase of this system could be a candidate for the supersolid, a system that simultaneously exhibit spatial long-range order and superfluidity. By the employment of DMC and PIGS, we report finite supefluid and condensate fractions, both in the gas and the stripe phases. Then, the study is completed by performing finite temperature calculations, where the use of PIMC allows to characterize the BKT transition and to report the critical temperature at which it occurs in the different phases. Finally, by direct comparison with the predictions of the Luttinger Liquid theory, we explicitly show that the stripe phase can not be described as an ensemble of 1D isolated systems.
In chapter 4, we study the fermionic dipolar system in two dimensions, focusing in the case in which all dipoles are polarized along the direction, that in this case is chosen to be the one perpendicular to the plane containing their movement. We compute the equation of state of the system in a wide range of interaction parameters. In the low density regime, the comparison of our results for the dipolar model with those of a hard-disks one allows to determine the regime of universality. On the other hand, at higher densities ( and before crystallization), we discuss the issue of itinerant ferromagnetism, that is, the possibility of having a polarized phase as the ground state of the system. The repulsive Fermi polaron with dipolar interaction, that corresponds to the limit of ultralow concentration of impurities embebed in a fermionic bath is also studied. Here we determine the regime of universality for this problem and compute observables that allow to discuss the validity of the quasi-particle picture.
In the last part of the thesis, the formation of ultra-dilute dipolar droplets is studied. Our results are in agreement with experimental measurements performed with dysprosium atoms. On the other hand, the evaluation of their differences with the prediction of the extended Gross-Pitaevskii equation makes it possible to determine the limits of the mean-field approach to this problem.El objeto de estudio de esta tesis son los sistemas dipolares en el régimen cuántico degenardo. Usualmente, tratar con sistemas de muchos cuerpos y para evaluar sus propiedades requiere ser capaz de resolver la ecuación de Schrödinger. En el presente estudio, empleamos diferentes métodos de Monte Carlo, que permiten encontrar soluciones numéricas de forma estocásticas. La primera y más simple de estas técnicas es el método Variational Monte Carlo (VMC), que da una solución variacional. Una mejora sobre lo anterior consiste en emplear el método Diffusion Monte Carlo (DMC) que permite obtener soluciones exactas para el estado fundamental del sistema (cuando se estudian sistemas bosónicos). Continuamos presentando dos métodos que se basan en el formalismo Feynman de la mecánica cuántica: Path Integral Monte Carlo (PIMC) y Path Integral Ground State (PIGS), que proporcionan soluciones exactas para el problema bosónico a temperatura finita y en el límite de temperatura cero respectivamente. Para trabajar con sistemas fermionicos, como es el caso del capítulo 4 de esta tesis, el algoritmo DMC tiene que ser modificado según la prescripción Fixed-Node para evitar el problema del signo. Al hacerlo, los resultados obtenidos con DMC se corresponden a soluciones variacionales a la energía. En el capítulo 3 estudiamos las propiedades superfluidas de un sistema de bosones dipolares completamente polarizados y en el que el movimiento de los dipolos está restringido al plano. También consideramos que los momentos dipolares forman un cierto ángulo con el eje perpendicular al plano, lo que permite introducir anisotropía en el sistema. El diagrama de fases a temperatura cero de este sistema revela la existencia de tres fases diferentes: gas, stripe y sólido. Aquí nos centramos en la caracterización de las propiedades superfluidas en ese diagrama de fases. Nuestros cálculos permiten abordar la cuestión de si la fase stripe de este sistema podría ser un candidato para el supersólido: un sistema en el que dos simetrías U (1) se rompen simultáneamente, permitiendo al sistema exhibir orden espacial de largo alcance y a la vez ser superfluido. Mediante el empleo de DMC y PIGS, evaluamos la fracción superfluída y el condensado, tanto en las fases de gas como en el stripe. Este estudio se completa con la extensión a temperatura finita, donde el uso de PIMC permite caracterizar la transición superfluida y obtener la temperatura crítica a la que ésta ocurre en las fases gas y stripe. Finalmente, por comparación directa con las predicciones Líquido de Luttinger, mostramos explícitamente que la fase de stripe no puede describirse como un conjunto de sistemas 1D aislados. En el capítulo 4, estudiamos el sistema dipolar fermiónico en dos dimensiones, enfocándonos en el caso en que todos los dipolos están polarizados a lo largo de la dirección que es perpendicular al plano que contiene su movimiento. Calculamos la ecuación de estado del sistema en un amplio rango de parámetros de interacción: a baja densidad, la comparación de nuestro modelo dipolar con uno de discos duros permite determinar el régimen de universalidad, mientras que a densidades más altas (antes de la cristalización), discutimos la posibilidad de una fase polarizada como el estado fundamental del sistema (ferromagnetismo itinerante). El polaron fermiónico dipolar, correspondiente al límite de impurezas ultradiluídas en un baño fermiónico también es estudiado, determinando el régimen de universalidad y los límites de validez de la aproximación de quasi-partícula. En la última parte de la tesis, la formación de gotas dipolares ultradiluídas es estudiada. Nuestros resultados están en acuerdo con medidas experimentales con átomos de disprosio. Por otro lado, la evaluación de las diferencias entre éstos y la predicción dada por la ecuación de Gross-Pitaevskii extendida, permite evaluar los límites de la aproximación
47
Lee, Robert. "Application of quantum Monte Carlo methods to excitonic and electronic systems". Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/239379.
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The work in this thesis is concerned with the application and development of quantum Monte Carlo (QMC) methods. We begin by proposing a technique to maximise the efficiency of the extrapolation of DMC results to zero time step, finding that a relative time step ratio of 1:4 is optimal. We discuss the post-processing of QMC data and the calculation of accurate error bars by reblocking, setting out criteria for the choice of block length. We then quantify the effects of uncertainty in the correlation length on estimated error bars, finding that the frequency of outliers is significantly increased for short runs. We then report QMC calculations of biexciton binding energies in bilayer systems. We have also calculated exciton-exciton interaction potentials, and radial distribution functions for electrons and holes in bound biexcitons. We find a larger region of biexciton stability than other recent work [C. Schindler and R. Zimmermann, Phys. Rev. B 78,045313 (2008)]. We also find that individual excitons retain their identity in bound biexcitons for large layer separations. Finally, we give details of a QMC study of the one-dimensional homogeneous electrongas (1D HEG). We present calculations of the energy, pair correlation function, static structure factor (SSF), and momentum density (MD) for the 1D HEG. We observe peaks in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around the Fermi wave vector, finding good agreement between the exponents of the ferromagnetic infinitely-thin and harmonic wires.
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Wiegand, Carsten [Verfasser]. "Optimal Monte Carlo and Quantum Algorithms for Parametric Integration / Carsten Wiegand". Aachen : Shaker, 2006. http://d-nb.info/1186586796/34.
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Lin, Fei Berlinsky A. J. Kallin C. Sørensen Erik S. "A quantum Monte Carlo study on the fullerene molecules and solids". *McMaster only, 2006.
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Oriols, Pladevall Xavier. "Quantum Monte Carlo simulation of tunnelling devices using wavepackets and Bohm trajectories". Doctoral thesis, Universitat Autònoma de Barcelona, 1999. http://hdl.handle.net/10803/5353.
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