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Journal articles on the topic 'Quantum Monte Carlo Technique'

Author: Grafiati

Published: 7 September 2023

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1

Marcu, Mihail, and Jürgen Müller. "Variance reduction technique for quantum Monte Carlo simulations." Physics Letters A 119, no. 3 (December 1986): 130–32. http://dx.doi.org/10.1016/0375-9601(86)90430-5.

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2

Jacoboni, C., P. Lugli, R. Brunetti, and L. Reggiani. "A Monte Carlo technique for quantum transport in semiconductors." Superlattices and Microstructures 2, no. 3 (January 1986): 209–12. http://dx.doi.org/10.1016/0749-6036(86)90021-2.

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3

Montanaro, Ashley. "Quantum speedup of Monte Carlo methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (September 2015): 20150301. http://dx.doi.org/10.1098/rspa.2015.0301.

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Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

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4

GUBERNATIS, J. E., and W. R. SOMSKY. "PARALLELIZATION OF THE WORLDLINE QUANTUM MONTE CARLO METHOD." International Journal of Modern Physics C 03, no. 01 (February 1992): 61–78. http://dx.doi.org/10.1142/s0129183192000063.

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The worldline quantum Monte Carlo method is a computational technique for studying the properties of many-electron and quantum-spin systems. In this paper, we describe our efforts in developing an efficient implementation of this method for the massively-parallel Connection Machine CM-2. We discuss why one must look beyond the obvious parallelism in the method in order to reduce interprocessor communication and increase processor utilization, and how these goals may be achieved using a plaquette-based data representation. We also present performance statistics for our implementation and sample calculations for the spinless fermion model.

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5

Moodley, Mervlyn. "The Lognormal Distribution and Quantum Monte Carlo Data." Communications in Computational Physics 15, no. 5 (May 2014): 1352–67. http://dx.doi.org/10.4208/cicp.190313.171013a.

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AbstractQuantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method entails reconstructing the probability distribution of a set of data, with given mean and variance, that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation. In doing so, we perform a numerical evaluation of the renormalized sum of lognormal random variables. This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

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6

Berg, Erez, Samuel Lederer, Yoni Schattner, and Simon Trebst. "Monte Carlo Studies of Quantum Critical Metals." Annual Review of Condensed Matter Physics 10, no. 1 (March 10, 2019): 63–84. http://dx.doi.org/10.1146/annurev-conmatphys-031218-013339.

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Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.

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7

Jiang, Weilun, Gaopei Pan, Yuzhi Liu, and Zi-Yang Meng. "Solving quantum rotor model with different Monte Carlo techniques." Chinese Physics B 31, no. 4 (April 1, 2022): 040504. http://dx.doi.org/10.1088/1674-1056/ac4f52.

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We systematically test the performance of several Monte Carlo update schemes for the (2 + 1)d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) schemes, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z 2 topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

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8

Alfè, D., and M. J. Gillan. "Linear-scaling quantum Monte Carlo technique with non-orthogonal localized orbitals." Journal of Physics: Condensed Matter 16, no. 25 (June 8, 2004): L305—L311. http://dx.doi.org/10.1088/0953-8984/16/25/l01.

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9

Rai, R. K., R. B. Ray, G. C. Kaphle, and O. P. Niraula. "A Continuous Time Quantum Monte Carlo as an Impurity Solver for Strongly Correlated System." Journal of Nepal Physical Society 7, no. 3 (December 31, 2021): 14–26. http://dx.doi.org/10.3126/jnphyssoc.v7i3.42185.

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We assess the continuous-time quantum Monte Carlo (CT-QMC) technique with hybridization expansion for solvingthe electronic structure of the strongly correlated system LaxSr1−xVO3 . The impurity solver method implemented here shows the fair agreement with the other available Monte Carlo techniques. From the study, it is found that the CT-QMC technique clearly distinguishes metallic phase, quasiparticle phase and insulating phases of the system depending upon the strength of the correlation. In case of La0.33Sr0.67VO3 system the metal-insulator transition is found to be at U = 4.5 eV for β = 6(eV)−1. The value of U depends with the value of β, and also the value of Hund’s coupling (J) and bandwidth (W). This technique allows the particle to exchange with the reservoir of the particles and the impurity sites, which is accounted numerically to treat the temporal fluctuation of the fermionic systems termed as dynamical mean field theory (DMFT). This theory is used to explain the phenomena of MottHubbard metal insulator transition of the materials which are applicable for designing the Mottronics, Neuromorphic computing, Quantum computing and resistive memory devices.

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10

Dowling, Mark R., Matthew J. Davis, Peter D. Drummond, and Joel F. Corney. "Monte Carlo techniques for real-time quantum dynamics." Journal of Computational Physics 220, no. 2 (January 2007): 549–67. http://dx.doi.org/10.1016/j.jcp.2006.05.017.

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11

AOUATI, REDHA, and ABDELKADER NOUIRI. "MONTE CARLO CALCULATION FOR CATHODOLUMINESCENCE OF AlGaAs/GaAs NANOSTRUCTURE." International Journal of Nanoscience 10, no. 03 (June 2011): 373–79. http://dx.doi.org/10.1142/s0219581x11008101.

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The cathodoluminescence technique (CL) performed in the Scanning Electron Microscope (SEM) offers opto-electronic characterization of some nanostructures and it is a powerful tool for studying the compositional variation or band structure of three-dimensional microscale or nanoscale structures. The major problem of the CL technique is the difficulty of high spatial resolution of the low-dimensional structure. In the present paper we propose a simple Monte Carlo calculation model to describe the interaction of electron beam with Al x Ga 1-x As - GaAs nanostructure. This model takes into account the confinement phenomenon in the quantum well by an easy method. The influence of different parameters such as the thickness of barriers, Al mole fraction (x), and the diffusion length are studied. The carrier excess generated during the collision of the incident electron with the atoms of the material (random walk) is calculated taking into account the confinement phenomenon within the quantum well. The radiative recombination of electron–hole pairs is collected as a light (CL signal).

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12

Sorella, S. "MONTE CARLO STUDY OF ONE HOLE IN A QUANTUM ANTIFERROMAGNET." International Journal of Modern Physics B 06, no. 05n06 (March 1992): 587–88. http://dx.doi.org/10.1142/s0217979292000360.

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Using the standard Quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a Quantum Antiferromagnet. The calculation is very well stabilized, using selected sized systems and special use of the trial wavefunction that satisfy the “close shell condition” in presence of an arbitrarily weak Zeeman magnetic field, vanishing in the thermodynamic limit. It will be shown in a forthcoming publication1 that the presence of this magnetic field does not affect thermodynamic properties for the half filled system. Then I have used the same selected sizes for the one hole ground state. I have investigated the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator should behave just as conventional insulator with an upper and lower Hubbard band. By comparing the present finite size scaling with several techniques predicting a finite quasiparticle weight (see Fig.1) the data seem more consistent with a vanishing quasiparticle weight, i.e. , as recently suggested by P.W. Anderson2 the Hubbard-Mott insulator should be characterized by non-trivial excitations which cannot be interpreted in a simple quasi-particle picture. However it cannot be excluded , based only on numerical grounds, that a very small but non vanishing quasiparticle weight should survive in the thermodynamic limit.

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13

MIYASHITA, Seiji, and Tota NAKAMURA. "MONTE CARLO STUDIES ON FRUSTRATED QUANTUM SPIN SYSTEMS BY A NEW APPROACH TO THE NEGATIVE-SIGN PROBLEM: TRANSFER-MATRIX MONTE CARLO METHOD." International Journal of Modern Physics C 07, no. 03 (June 1996): 425–31. http://dx.doi.org/10.1142/s0129183196000375.

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A new technique for the negative sign problem in the quantum Monte Carlo method using the Suzuki-Trotter decomposition is introduced. In order to reduce the cancellation between between samples with positive and negative weights, we make use of the transfer matrix method, which has been named the Transfer-Matrix Monte Carlo method. Applications to the Heisenberg antiferromagnet on the ∆-chain and on the kagome lattice, and also to the Kondo lattice system also are given.

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14

Benedek, Nicole A., Irene Yarovsky, Kay Latham, and Ian K. Snook. "Quantum Monte Carlo Study of Water Molecule: A Preliminary Investigation." Australian Journal of Chemistry 57, no. 12 (2004): 1229. http://dx.doi.org/10.1071/ch04135.

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The Quantum Monte Carlo (QMC) technique[1] offers advantages of good scaling with system size (number of electrons) and an ability to uniformly recover over 90% of the electron correlation energy, compared to the more conventional quantum chemistry approaches. For the water molecule in its ground state, it has been shown[2] that the QMC method gives results that are comparable in accuracy to those obtained by the best available conventional methods, while at the same time using much more modest basis sets than is necessary with these methods. Furthermore, the effect of the orbitals needed for these QMC calculations (which may be obtained from either Hartree–Fock or Density Functional Theory) has been investigated. Both the advantages and disadvantages of the QMC method are discussed.

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15

Harowitz, Matthew, Daejin Shin, and John Shumway. "Path-Integral Quantum Monte Carlo Techniques for Self-Assembled Quantum Dots." Journal of Low Temperature Physics 140, no. 3-4 (July 25, 2005): 211–26. http://dx.doi.org/10.1007/s10909-005-6309-6.

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16

BONČA, J., C. D. BATISTA, J. E. GUBERNATIS, and H. Q. LIN. "ELECTRONICALLY DRIVEN FERROELECTRICITY IN THE EXTENDED FALICOV-KIMBALL MODEL." International Journal of Modern Physics B 19, no. 01n03 (January 30, 2005): 525–27. http://dx.doi.org/10.1142/s0217979205028967.

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We calculate the quantum phase diagram of an extended Falicov-Kimball model in the intermediate coupling regime using a constrained path quantum Monte Carlo technique. The mixed-valence regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization.

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17

Barnett, R. N., and K. B. Whaley. "Variational and diffusion Monte Carlo techniques for quantum clusters." Physical Review A 47, no. 5 (May 1, 1993): 4082–98. http://dx.doi.org/10.1103/physreva.47.4082.

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18

Xu, Xiao Yan, Zi Hong Liu, Gaopei Pan, Yang Qi, Kai Sun, and Zi Yang Meng. "Revealing fermionic quantum criticality from new Monte Carlo techniques." Journal of Physics: Condensed Matter 31, no. 46 (August 19, 2019): 463001. http://dx.doi.org/10.1088/1361-648x/ab3295.

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19

Winstead, B., and U. Ravaioli. "Simulation of Schottky barrier MOSFETs with a coupled quantum injection/Monte Carlo technique." IEEE Transactions on Electron Devices 47, no. 6 (June 2000): 1241–46. http://dx.doi.org/10.1109/16.842968.

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20

Berner, Raphael, René Petz, and Arne Lüchow. "Towards Correlated Sampling for the Fixed-Node Diffusion Quantum Monte Carlo Method." Zeitschrift für Naturforschung A 69, no. 7 (July 1, 2014): 279–86. http://dx.doi.org/10.5560/zna.2014-0002.

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Most methods of quantum chemistry calculate total energies rather than directly the energy differences that are of interest to chemists. In the case of statistical methods like quantum Monte Carlo the statistical errors in the absolute values need to be considerably smaller than their difference. The calculation of small energy differences is therefore particularly time consuming. Correlated sampling techniques provide the possibility to compute directly energy differences by simulating the underlying systems with the same stochastic process. The smaller the energy difference the smaller its statistical error. Correlated sampling is well established in variational quantum Monte Carlo, but it is much more difficult to implement in diffusion quantum Monte Carlo because of the fixed node approximation. A correlated sampling formalism and a corresponding algorithm based on a transformed Schrödinger equation having the form of a Kolmogorov’s backward equation is derived. The numerical verification of the presented algorithm is given for the harmonic oscillator. The extension of the algorithm to electron structure calculations is discussed.

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21

SHARMA, MEENAKSHI, KAMLESH KUMARI, and ISHWAR SINGH. "QUANTUM MONTE CARLO SIMULATION STUDY OF ONE-DIMENSIONAL PERIODIC ANDERSON MODEL." International Journal of Modern Physics B 13, no. 32 (December 30, 1999): 3927–42. http://dx.doi.org/10.1142/s0217979299004094.

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Many rare earth and actinide intermetallics, known as Heavy Fermion Systems, have recently been successfully described by the Periodic Anderson Model. We investigate, in this work, various electronic and magnetic properties of the one-dimensional Periodic Anderson model using path integral formulation along with the quantum Monte Carlo simulation technique. We have studied the singlet and triplet pairing correlation functions, nearest neighbor charge-density correlations, spin density correlations, local squared magnetic moment and probability of double occupancy of f-electrons, as a function of intra-atomic Coulomb interaction for various values of hybridization parameter and the temperatures.

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22

Kaur, Amandeep, Satnam Kaur, and Gaurav Dhiman. "A quantum method for dynamic nonlinear programming technique using Schrödinger equation and Monte Carlo approach." Modern Physics Letters B 32, no. 30 (October 30, 2018): 1850374. http://dx.doi.org/10.1142/s0217984918503748.

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The power of quantum computing may allow for solving the problems which are not practically feasible on classical computers and suggest a considerable speed up to the best known classical approaches. In this paper, we present the contemporary quantum behaved approach which is based on Schrödinger equation and Monte Carlo method. The three basic steps of proposed technique are also mathematically modeled and discussed for effective movement of particles. The performance of the proposed approach is tested for solving the dynamic nonlinear problem. Experimental results reveal the supremacy of proposed approach for solving the nonlinear problem as compared to other approaches.

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23

MARKIĆ, LEANDRA VRANJEŠ, JORDI BORONAT, JOAQUIM CASULLERAS, and CALUDIO CAZORLA. "QUANTUM MONTE CARLO STUDY OF OVERPRESSURIZED LIQUID 4He AT ZERO TEMPERATURE." International Journal of Modern Physics B 20, no. 30n31 (December 20, 2006): 5154–63. http://dx.doi.org/10.1142/s0217979206036211.

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We present a diffusion Monte Carlo simulation of metastable superfluid 4 He at zero temperature and pressures beyond freezing (~ 25 bar) up to 275 bar. The equation of state of liquid 4 He is extended to the overpressurized regime, where the pressure dependence of the static structure factor and the condensate fraction is obtained. Along this large pressure range, excited-state energy corresponding to the roton has been determined using the release-node technique. Our results show that both the roton energies and the condensate fraction decrease with increasing pressure but do not become zero. We compare our calculations to recent experimental data in overpressurized regime.

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24

Husslein, Thomas, Werner Fettes, and Ingo Morgenstern. "Comparison of Calculations for the Hubbard Model Obtained with Quantum-Monte-Carlo, Exact, and Stochastic Diagonalization." International Journal of Modern Physics C 08, no. 02 (April 1997): 397–415. http://dx.doi.org/10.1142/s0129183197000333.

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In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with results from exact and stochastic diagonalizations. We find good agreement for the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on the superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by fluctuations or systematic errors of the method. Although we notice that the Quantum-Monte-Carlo method has convergence problems for large interactions, coinciding with a minus sign problem, we confirm the results of the diagonalization techniques for small and moderate interaction strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive case, to study the influence of the minus sign problem on convergence. Also here in the absence of a minus sign problem we encounter convergence problems for strong interactions.

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25

Tsuchiya, Hideaki, Brian Winstead, and Umberto Ravaioli. "Quantum Potential Approaches for Nano-scale Device Simulation." VLSI Design 13, no. 1-4 (January 1, 2001): 335–40. http://dx.doi.org/10.1155/2001/73145.

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With the progress of integrated technology, the feature size of experimental electron devices have already been scaled down deeply into the sub–0.1 μm region. For such ultra-small devices, it is increasingly important to take quantum mechanical effects into account for device simulation. In this paper, we present a new approach for quantum modeling, applicable to multi-dimensional ultra-small device simulation. In this work, the quantum effects are represented in terms of quantum mechanically corrected potential in the classical Boltzmann equation. We apply the Monte Carlo method to solve the quantum transport equation, and demonstrate that the quantum effects such as tunneling and quantum confinement effects can be incorporated in the standard Monte Carlo techniques.

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26

Bordone, P., A. Bertoni, R. Brunetti, and C. Jacoboni. "Wigner Paths Method in Quantum Transport with Dissipation." VLSI Design 13, no. 1-4 (January 1, 2001): 211–20. http://dx.doi.org/10.1155/2001/80236.

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The concept of Wigner paths in phase space both provides a pictorial representation of the quantum evolution of the system of interest and constitutes a useful tool for numerical solutions of the quantum equation describing the time evolution of the system. A Wigner path is defined as the path followed by a “simulative particle” carrying a σ-contribution of the Wigner function through the Wigner phase-space, and is formed by ballistic free flights separated by scattering processes (both scattering with phonons and with an arbitrary potential profile can be included), as for the case of semiclassical particles. Thus, the integral transport equation can be solved by a Monte Carlo technique by means of simulative particles following classical trajectories, in complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation in the integral form.

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27

Ramasubramaniam, Ashwin, and Emily A. Carter. "Coupled Quantum–Atomistic and Quantum–Continuum Mechanics Methods in Materials Research." MRS Bulletin 32, no. 11 (November 2007): 913–18. http://dx.doi.org/10.1557/mrs2007.188.

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AbstractThe interface of quantum mechanics methods with classical atomistic simulation techniques, such as molecular dynamics and Monte Carlo, continues to be an area of considerable promise and interest. Such coupled quantum–atomistic approaches have been developed and employed, for example, to gain a comprehensive understanding of the energetics, kinetics, and dynamics of chemical processes involving surfaces and interfaces of hard materials. More recently, it has become possible to directly couple first-principles electronic structure techniques to continuum solid mechanics, either on the fly with feedback between length scales or by information passing between length scales. We discuss, with tutorial examples, the merging of quantum mechanics with molecular dynamics and Monte Carlo simulations, as well as quantum–continuum coupled techniques. We illustrate the opportunities offered by incorporation of information from quantum mechanics (reducing assumptions in higher length-scale models) and outline the challenges associated with achieving full predictive capability for the behavior of materials.

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28

VIEL, ALEXANDRA, and K. BIRGITTA WHALEY. "STRUCTURE AND SPECTROSCOPY OF DOPED HELIUM CLUSTERS USING QUANTUM MONTE CARLO TECHNIQUES." International Journal of Modern Physics B 17, no. 28 (November 10, 2003): 5267–77. http://dx.doi.org/10.1142/s0217979203020405.

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We present a comparative study of the rotational characteristics of various molecule-doped 4 He clusters using quantum Monte Carlo techniques. The theoretical conclusions obtained from both zero and finite temperature Monte Carlo studies confirm the presence of two different dynamical regimes that correlate with the magnitude of the rotational constant of the molecule, i.e. fast or slow rotors. For a slow rotor, the effective rotational constant for the molecule inside the helium droplet can be determined by a microscopic two-fluid model in which helium densities computed by path integral Monte Carlo are used as input, as well as by direct computation of excited energy levels. For a faster rotor, the conditions for application of the two-fluid model for dynamical analysis are usually not fulfilled and the direct determination of excitation energies is then mandatory. Quantitative studies for three molecules are summarised, showing in each case excellent agreement with experimental results.

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29

Pandey, Devashish, Enrique Colomés, Guillermo Albareda, and Xavier Oriols. "Stochastic Schrödinger Equations and Conditional States: A General Non-Markovian Quantum Electron Transport Simulator for THz Electronics." Entropy 21, no. 12 (November 25, 2019): 1148. http://dx.doi.org/10.3390/e21121148.

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A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schrödinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction (linked to the corresponding Bohmian trajectory) as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of freedom. As an example of the practical utility of these states, we present a time-dependent quantum Monte Carlo algorithm to describe electron transport in open quantum systems under general (Markovian or non-Markovian) conditions. By making the most of trajectory-based and wavefunction methods, the resulting simulation technique extends to the quantum regime, the computational capabilities that the Monte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.

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30

Honma, Michio, Takahiro Mizusaki, and Takaharu Otsuka. "Diagonalization of Hamiltonians for Many-Body Systems by Auxiliary Field Quantum Monte Carlo Technique." Physical Review Letters 75, no. 7 (August 14, 1995): 1284–87. http://dx.doi.org/10.1103/physrevlett.75.1284.

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31

YILDIZ, A., S. ŞAKİROĞLU, Ü. DOĞAN, K. AKGÜNGÖR, H. EPİK, İ. SÖKMEN, H. SARI, and Y. ERGÜN. "VARIATIONAL COMPUTATIONS FOR EXCITONS IN QUANTUM DOTS: A QUANTUM MONTE CARLO STUDY." International Journal of Modern Physics B 25, no. 01 (January 10, 2011): 119–30. http://dx.doi.org/10.1142/s0217979211055683.

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A study of variational wave functions for calculation of the ground-state energies of excitons confined in a two-dimensional (2D) disc-like and three-dimensional (3D) spherical parabolic GaAs quantum dots (QDs) is presented. We have used four variational trial wave functions constructed as the harmonic-oscillator basis multiplied by different correlation functions. The proposed correlation function formed by including linear expansion in terms of Hylleraas-like coordinates to the Jastrow factor is able to capture nearly exactly the ground-state energies of 3D excitons, and it properly account for the results of 2D excitons. Quantum Monte Carlo techniques combined with the proposed wave function are a powerful tool for studying excitons in parabolic QDs.

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32

Konev, Vitaly, Evgeny Vasinovich, Vasily Ulitko, Yury Panov, and Alexander Moskvin. "Unconventional phase transitions in strongly anisotropic 2D (pseudo)spin systems." EPJ Web of Conferences 185 (2018): 08006. http://dx.doi.org/10.1051/epjconf/201818508006.

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We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 (pseudo)spin system to find the ground state phase with its evolution under application of the (pseudo)magnetic field. The comparison of the two methods allows us to clearly demonstrate the role of quantum effects. Special attention is given to the role played by an effective single-ion anisotropy ("on-site correlation").

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33

Storer, RG. "Structure of Quantum Fluids at Nonzero Temperature." Australian Journal of Physics 44, no. 3 (1991): 305. http://dx.doi.org/10.1071/ph910305.

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A method is presented for the calculation of the structure of fluids and gases, such as He, Ne or H2, for which quantum effects are important. The method depends on finding an efficient Monte Carlo sampling technique to evaluate the appropriate averages which lead to the radial distribution function. The method is illustrated by results for the radial distribution function of helium and neon at finite temperatures and densities.

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34

SCHMIDT, K. E., and D. M. CEPERLEY. "ChemInform Abstract: Monte Carlo Techniques for Quantum Fluids, Solids and Droplets." ChemInform 23, no. 51 (December 22, 1992): no. http://dx.doi.org/10.1002/chin.199251346.

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35

Muscato, Orazio. "A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation." Communications in Applied and Industrial Mathematics 8, no. 1 (December 20, 2017): 237–50. http://dx.doi.org/10.1515/caim-2017-0012.

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Abstract The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.

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36

Yuan, Shunyue, Yueqing Chang, and Lucas K. Wagner. "Quantification of electron correlation for approximate quantum calculations." Journal of Chemical Physics 157, no. 19 (November 21, 2022): 194101. http://dx.doi.org/10.1063/5.0119260.

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State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.

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37

LIN, HAI QING, and JUN LI. "Frustration Effects in the Two-Dimensional Hubbard Model." International Journal of Modern Physics B 13, no. 29n31 (December 20, 1999): 3552–54. http://dx.doi.org/10.1142/s0217979299003404.

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We discuss frustration effects by studying the two-dimensional Hubbard model with nearest-neighbor(t) and next-nearest-neighbor(t′) hoppings. We present results obtained by the mean-field solution, the exact diagonalization technique, and the quantum Monte Carlo simulations. Questions to be addressed are: (1) magnetic phase diagram; (2) domain formation; and (3) superconducting pair correlation functions.

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38

Lee, Dean. "THE ROLE OF DIAGONALIZATION WITHIN A DIAGONALIZATION/MONTE CARLO SCHEME." International Journal of Modern Physics A 16, supp01c (September 2001): 1245–47. http://dx.doi.org/10.1142/s0217751x01009430.

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We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.

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DATTA, S. "THERMODYNAMIC PROPERTIES OF A TRAPPED BOSE GAS: A DIFFUSION MONTE CARLO STUDY." International Journal of Modern Physics B 22, no. 24 (September 30, 2008): 4261–73. http://dx.doi.org/10.1142/s021797920804870x.

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We investigate the thermodynamic properties of a trapped Bose gas of Rb atoms interacting through a repulsive potential at low but finite temperature (kBT < μ < Tc) by Quantum Monte Carlo method based upon the generalization of Feynman-Kac method1-3 applicable to many-body systems at T=0 to finite temperatures. In this paper, we report temperature variation of condensation fraction, chemical potential, density profile, total energy of the system, release energy, frequency shifts and moment of inertia within the realistic potential model (Morse type) for the first time by diffusion Monte Carlo technique. The most remarkable success was in achieving the same trend in the temperature variation of frequency shifts as was observed in JILA4 for both m=2 and m=0 modes. For other things, we agree with the work of Giorgini et al.,5 Pitaevskii et al.6 and Krauth.7

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Acevedo, Orlando, and Wiliiam L. Jorgensen. "Quantum and molecular mechanical Monte Carlo techniques for modeling condensed-phase reactions." Wiley Interdisciplinary Reviews: Computational Molecular Science 4, no. 5 (February 12, 2014): 422–35. http://dx.doi.org/10.1002/wcms.1180.

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Muscato, Orazio, and Vincenza Di Stefano. "Wigner Monte Carlo simulation without discretization error of the tunneling rectangular barrier." Communications in Applied and Industrial Mathematics 10, no. 1 (January 1, 2019): 20–30. http://dx.doi.org/10.2478/caim-2019-0009.

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Abstract The Wigner transport equation can be solved stochastically by Monte Carlo techniques based on the theory of piecewise deterministic Markov processes. A new stochastic algorithm, without time discretization error, has been implemented and studied in the case of the quantum transport through a rectangular potential barrier.

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ROJDESTVENSKI, I. V., M. G. COTTAM, I. A. FAVORSKI, T. KUZNETSOVA, and P. N. VORONTSOV-VELYAMINOV. "MONTE CARLO SIMULATION OF THE CRITICAL PROPERTIES OF QUASI-TWO-DIMENSIONAL QUANTUM HEISENBERG SYSTEMS." Surface Review and Letters 01, no. 02n03 (August 1994): 239–52. http://dx.doi.org/10.1142/s0218625x94000242.

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The critical properties of spin S=1/2 isotropic Heisenberg ferromagnetic ultrathin films are investigated using the Handscomb Monte Carlo technique. We study a simple cubic lattice with nearest neighbor interactions, including the effects of different values for the interlayer and intralayer exchange parameters. The number of monolayers is taken as 1, 2, or 3, and also we examine the effects of dilution in one of the layers. Numerical calculations are presented for the critical behavior of the longitudinal susceptibility and the spin correlation range. The results are interpreted in terms of a two-dimensional type of critical behavior with renormalized (modified) exchange parameters.

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Mamand, Dyari Mustafa, Yousif Hussein Azeez, and Hiwa Mohammad Qadr. "Monte Carlo and DFT calculations on the corrosion inhibition efficiency of some benzimide molecules." Mongolian Journal of Chemistry 24, no. 50 (June 5, 2023): xx. http://dx.doi.org/10.5564/mjc.v24i50.2435.

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Calculations using density functional theory (DFT) and Monte Carlo methods were performed on 2-methylbenzimidazole, 2-mercaptobenzimidazole, 2-aminobenzimidazole, benzotriazole, and benzimidazole to determine their corrosion inhibition efficiency. The molecular structure was optimized geometrically using DFT calculations at the B3LYP/6– 311 G++(d,p) and b2plypd3/aug-cc-pvdz basis set level in protonated and non-protonated species in gas and water. In this study, HOMO, LUMO, bandgap, ionization energy, electronegativity, hardness, softness, electrophilicity and nucleophilicity, electron transfer, back donation energy and condensed Fukui indices are used to assess a molecule's local reactivity. Theoretical investigations can precisely establish the geometrical dimensions of a molecule and correctly explain the quantum properties of inhibitors. The mechanism of interaction between inhibitors and metal surfaces in a specified molecule is studied using molecular dynamics. The benzimidazole functional groups absorbed energy linearly on metal surfaces, with quantum characteristics determined using density functional theory and an ab initio technique. Importantly, the findings of this conceptual model are consistent with the corrosion inhibition efficiency of earlier experimental investigations.

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Bakry, Ahmed S., Xurong Chen, and Pengming Zhang. "Noise reduction by combining smearing with multi-level integration methods." International Journal of Modern Physics E 23, no. 06 (June 2014): 1460008. http://dx.doi.org/10.1142/s0218301314600088.

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In this paper, we propose an algorithm that combines the Lüscher–Weiss (LW) multi-level error reduction technique with three-dimensional gauge-field smoothing. The purpose of this algorithm is to reduce the noise and the computational time associated with measuring field correlators in the low temperature pure quantum chromodynamics (QCD), or the stringy regions of Yang–Mills theory in general. The simultaneous application of both link-blocking and path-integral factorization techniques is based on the observation that Monte Carlo updating of the three-dimensional smeared lattices preserves the key features of the long distance physics.

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Garmer, David R. "Extrapolation of the time-step bias in diffusion quantum Monte Carlo by a differential sampling technique." Journal of Computational Chemistry 10, no. 2 (March 1989): 176–85. http://dx.doi.org/10.1002/jcc.540100205.

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46

Yoder, P. D., U. Krumbein, K. Gärtner, N. Sasaki, and W. Fichtner. "Statistical Enhancement of Terminal Current Estimation for Monte Carlo Device Simulation." VLSI Design 6, no. 1-4 (January 1, 1998): 303–6. http://dx.doi.org/10.1155/1998/34726.

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We present a new generalized Ramo-Shockley theorem (GRST) to evaluate contact currents, applicable to classical moment-based simulation techniques, as well as semiclassical Monte Carlo and quantum mechanical transport simulation, which remains valid for inhomogeneous media, explicitly accounts for generation/recombination processes, and clearly distinguishes between electron, hole, and displacement current contributions to contact current. We then show how this formalism may be applied to Monte Carlo simulation to obtain equations for minimum-variance estimators of steady-state contact current, making use of information gathered from all particles within the device. Finally, by means of an example, we demonstrate this technique’s performance in acceleration of convergence time.

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Wheeler, William A., Shivesh Pathak, Kevin G. Kleiner, Shunyue Yuan, João N. B. Rodrigues, Cooper Lorsung, Kittithat Krongchon, et al. "PyQMC: An all-Python real-space quantum Monte Carlo module in PySCF." Journal of Chemical Physics 158, no. 11 (March 21, 2023): 114801. http://dx.doi.org/10.1063/5.0139024.

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We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

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KOSINA, HANS. "NANOELECTRONIC DEVICE SIMULATION BASED ON THE WIGNER FUNCTION FORMALISM." International Journal of High Speed Electronics and Systems 17, no. 03 (September 2007): 475–84. http://dx.doi.org/10.1142/s0129156407004667.

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Coherent transport in mesoscopic devices is well described by the Schrödinger equation supplemented by open boundary conditions. When electronic devices are operated at room temperature, however, a realistic transport model needs to include carrier scattering. In this work the kinetic equation for the Wigner function is employed as a model for dissipative quantum transport. Carrier scattering is treated in an approximate manner through a Boltzmann collision operator. A Monte Carlo technique for the solution of this kinetic equation has been developed, based on an interpretation of the Wigner potential operator as a generation term for numerical particles. Including a multi-valley semiconductor model and a self-consistent iteration scheme, the described Monte Carlo simulator can be used for routine device simulations. Applications to single barrier and double barrier structures are presented. The limitations of the numerical Wigner function approach are discussed.

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BISHOP, R. F., and D. J. J. FARNELL. "AB INITIO CALCULATIONS FOR THE SQUARE-LATTICE ANISOTROPIC HEISENBERG MODEL." International Journal of Modern Physics B 13, no. 05n06 (March 10, 1999): 709–19. http://dx.doi.org/10.1142/s0217979299000606.

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Interest in lattice quantum spin systems as models of quantum magnets has increased with the discovery of new and interesting magnetic materials. Here we use a well-known technique of quantum many-body theory, namely the coupled-cluster method (CCM), to investigate the nearest-neighbour, spin-½, anisotropic Heisenberg model on the square lattice. Ground-state expectation values for quantities such as the ground-state energy and the sublattice magnetisation are determined to an accuracy comparable with that of the best of other available techniques including Monte Carlo methods. In order to demonstrate this point we present results for various values of the anisotropy parameter, including those for the isotropic Heisenberg model and the isotropic XY model. We show that it is now possible to determine the presence and position of the quantum phase transitions using ab initio CCM calculations, and furthermore that we can accurately predict the critical behaviour at these points.

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Volkenandt, T., E. Müller, D. Z. Hu, D. M. Schaadt, and D. Gerthsen. "Quantification of Sample Thickness and In-Concentration of InGaAs Quantum Wells by Transmission Measurements in a Scanning Electron Microscope." Microscopy and Microanalysis 16, no. 5 (July 16, 2010): 604–13. http://dx.doi.org/10.1017/s1431927610000292.

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AbstractHigh-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images of electron-transparent samples show dominant atomic number (Z-) contrast with a high lateral resolution. HAADF STEM at low electron energies <30 keV is applied in this work for quantitative composition analyses of InGaAs quantum wells. To determine the local composition, normalized experimental image intensities are compared with results of Monte Carlo simulations. For verification of the technique, InGaAs/GaAs quantum-well structures with known In concentration are used. Transmission electron microscopy samples with known thickness are prepared by the focused-ion-beam technique. The method can be extended to other material systems and is particularly promising for the analysis of materials that are sensitive toward knock-on damage.

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