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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Giner, Emmanuel, Anthony Scemama, and Michel Caffarel. "Using perturbatively selected configuration interaction in quantum Monte Carlo calculations." Canadian Journal of Chemistry 91, no. 9 (September 2013): 879–85. http://dx.doi.org/10.1139/cjc-2013-0017.

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Анотація:

Defining accurate and compact trial wavefunctions leading to small statistical and fixed-node errors in quantum Monte Carlo (QMC) calculations is still a challenging problem. Here we propose to make use of selected configuration interaction (CI) expansions obtained by selecting the most important determinants through a perturbative criterion. A major advantage with respect to truncated CASSCF wavefunctions or CI expansions limited to a maximum number of excitations (e.g, CISD) is that much smaller expansions can be considered (many unessential determinants are avoided), an important practical point for efficient QMC calculations. The most important determinants entering first during the selection process (hierarchical construction) the main features of the nodal structure of the wavefunction can be expected to be obtained with a moderate number of determinants. Thanks to this property, the delicate problem of optimizing in a Monte Carlo framework the numerous linear and (or) nonlinear parameters of the determinantal part of the trial wavefunction could be avoided. As a first numerical example, the calculation of the ground-state energy of the oxygen atom is presented. The best DMC value reported so far is obtained.

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2

FRANJIĆ, FRANJO, and SANDRO SORELLA. "A VARIATIONAL STUDY OF FERMI AND LUTTINGER LIQUID WAVEFUNCTIONS IN THE TWO-DIMENSIONAL t-J MODEL." Modern Physics Letters B 10, no. 18 (August 10, 1996): 873–81. http://dx.doi.org/10.1142/s0217984996000997.

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Анотація:

Using a recently developed technique, we determine the Jastrow potential of the variational wavefunction for the two-dimensional t-J model. This wavefunction describes a Fermi liquid ground state and is compared with the Luttinger liquid wavefunction used by Gros and Valentí. Estimates of the energy of these states are calculated using the variational Monte Carlo technique, showing that the Fermi liquid state has a little power energy.

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3

Erkoc, S. "Wavefunction correction scheme for non fixed-node diffusion Monte Carlo." Journal of Atomic and Molecular Sciences 2, no. 1 (June 2011): 1–9. http://dx.doi.org/10.4208/jams.072810.082010a.

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4

Mcdowell, Keith. "Assessing the quality of a wavefunction using quantum monte carlo." International Journal of Quantum Chemistry 20, S15 (June 19, 2009): 177–81. http://dx.doi.org/10.1002/qua.560200818.

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5

Rao, Lu, and Fan Wang. "Diffusion quantum Monte Carlo method on diradicals using single- and multi-determinant-Jastrow trial wavefunctions and different orbitals." Journal of Chemical Physics 156, no. 12 (March 28, 2022): 124308. http://dx.doi.org/10.1063/5.0086606.

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In this work, the diffusion quantum Monte Carlo (DMC) method is employed to calculate the energies of singlet and triplet states for a series of organic diradicals and diatomic diradicals with π2 configuration. Single-determinant-Jastrow (SDJ) trial wavefunctions for triplet states, two-determinant-Jastrow (2DJ) trial wavefunctions for the singlet states, and multi-determinant-Jastrow (MDJ) trial wavefunctions are employed in DMC calculations using restricted open-shell B3LYP (ROB3LYP) orbitals, complete-active-space self-consistent field (CASSCF) orbitals, state-average CASSCF orbitals, or frozen-CASSCF orbitals. Our results show that DMC energies using either SDJ/2DJ or MDJ with ROB3LYP orbitals are close to or lower than those with the other orbitals for organic diradicals, while they are not very sensitive to the employed orbitals for diatomic diradicals. Furthermore, using MDJ can reduce DMC energies to some extent for most of the investigated organic diradicals and some diatomic diradicals. The importance of MDJ on DMC energies can be estimated based on the percentage of main determinants in the CASCI wavefunction. On the other hand, singlet–triplet gaps can be calculated reasonably with DMC using MDJ with a mean absolute error of less than 2 kcal/mol with all these orbitals. CASCI wavefunctions using density functional theory orbitals are preferred in constructing MDJ trial wavefunctions in practical DMC calculations since it is easier to obtain such wavefunctions than CASSCF methods.

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6

GROS, CLAUDIUS, and ROSER VALENTÍ. "LUTTINGER-LIQUID BEHAVIOUR IN 2D: THE VARIATIONAL APPROACH." Modern Physics Letters B 07, no. 03 (February 10, 1993): 119–41. http://dx.doi.org/10.1142/s0217984993000151.

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Анотація:

We study a variational formulation of the Luttinger-liquid concept in two dimensions. We show that a Luttinger-liquid wavefunction with an algebraic singularity at the Fermiedge is given by a Jastrow-Gutzwiller type wavefunction, which we evaluate by variational Monte Carlo for lattices with up to 38 × 38 = 1444 sites. We therefore find that, from a variational point of view, the concept of a Luttinger liquid is well defined even in 2D. We also find that the Luttinger liquid state is energetically favoured by the projected kinetic energy in the context of the 2D t-J model. We study and find coexistence of d-wave superconductivity and Luttinger-liquid behaviour in two-dimensional projected wavefunctions. We then argue that generally, any two-dimensional d-wave superconductor should be unstable against Luttinger-liquid type correlations along the (quasi-1D) nodes of the d-wave order parameter, at temperatures small compared to the gap.

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7

Samaras, M., and C. J. Hamer. "Forward-walking Green's Function Monte Carlo Method for Correlation Functions." Australian Journal of Physics 52, no. 4 (1999): 637. http://dx.doi.org/10.1071/ph98092.

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The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation Mz and the correlation function p z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.

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8

Nakano, Masayoshi, Kenji Okada, Takanori Nagami, Takayoshi Tonami, Ryohei Kishi, and Yasutaka Kitagawa. "Monte Carlo Wavefunction Approach to Singlet Fission Dynamics of Molecular Aggregates." Molecules 24, no. 3 (February 1, 2019): 541. http://dx.doi.org/10.3390/molecules24030541.

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Анотація:

We have developed a Monte Carlo wavefunction (MCWF) approach to the singlet fission (SF) dynamics of linear aggregate models composed of monomers with weak diradical character. As an example, the SF dynamics for a pentacene dimer model is investigated by considering the intermolecular electronic coupling and the vibronic coupling. By comparing with the results by the quantum master equation (QME) approach, we clarify the dependences of the MCWF results on the time step (Δt) and the number of MC trajectories (MC). The SF dynamics by the MCWF approach is found to quantitatively (within an error of 0.02% for SF rate and of 0.005% for double-triplet (TT) yield) reproduce that by the QME approach when using a sufficiently small Δt (~0.03 fs) and a sufficiently large MC (~105). The computational time (treq) in the MCWF approach also exhibits dramatic reduction with increasing the size of aggregates (N-mers) as compared to that in the QME approach, e.g., ~34 times faster at the 20-mer, and the size-dependence of treq shows significant reduction from N5.15 (QME) to N3.09 (MCWF). These results demonstrate the promising high performance of the MCWF approach to the SF dynamics in extended multiradical molecular aggregates including a large number of quantum dissipation, e.g., vibronic coupling, modes.

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9

Keens, Robert H., and Daniel R. Kattnig. "Monte-Carlo wavefunction approach for the spin dynamics of recombining radicals." New Journal of Physics 22, no. 8 (August 24, 2020): 083064. http://dx.doi.org/10.1088/1367-2630/aba76d.

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10

Riley, Kevin E., and James B. Anderson. "A new variational Monte Carlo trial wavefunction with directional Jastrow functions." Chemical Physics Letters 366, no. 1-2 (November 2002): 153–56. http://dx.doi.org/10.1016/s0009-2614(02)01530-0.

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11

XIAO, YINGSHENG, and BILL POIRIER. "USING DISCRETE VARIABLE REPRESENTATION PATH INTEGRAL MONTE CARLO WITH METROPOLIS SAMPLING TO COMPUTE GROUND STATE WAVEFUNCTIONS." Journal of Theoretical and Computational Chemistry 06, no. 02 (June 2007): 309–21. http://dx.doi.org/10.1142/s021963360700299x.

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Анотація:

The discrete variable representation (DVR) matrix dynamics formulation of the path integral Monte Carlo (PIMC) method, implemented numerically in a way that enables Metropolis sampling to be employed, is proposed as a means of computing ground state quantum wavefunctions. A key advantage of the DVR-PIMC approach is that customized marginal potentials may be employed, leading to significantly larger PIMC time step sizes, and substantial reductions in computational (CPU) effort. An additional key advantage of the present implementation is that the DVR provides a natural set of interpolant functions that can be used for accurate interpolation and extrapolation of function and tensor quantities away from predefined grid points. The new method is applied here to compute the ground state wavefunction of a model one degree-of-freedom (1 DOF) Morse oscillator system. A one-to-two order-of-magnitude reduction in CPU effort is observed, in comparison with a conventional PIMC simulation. The generalization for many DOFs is straightforward, and expected to result in even greater performance enhancement.

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12

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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Анотація:

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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13

Scholten, R. E., T. J. O'Kane, T. R. Mackin, T. A. Hunt, and P. M. Farrell. "Calculating Trajectories for Atoms in Near-resonant Lightfields." Australian Journal of Physics 52, no. 3 (1999): 493. http://dx.doi.org/10.1071/ph99014.

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Анотація:

We review several methods for calculating the time development of the internal state and the external motion of atoms in near-resonant light fields, with emphasis on studying the focussing of atomic beams into microscopic and potentially nanoscopic patterns. Three different approaches are considered: two-level semiclassical, multi-level semiclassical, and the Monte Carlo wavefunction method. The two-level semiclassical technique of McClelland and Scheinfein (1991) and McClelland (1995) is extended to three dimensions, and used to calculate the trajectories of atoms and the imaging properties of a simple lens formed from a near-resonant travelling TEM01 mode laser. The model is then extended to multi-level atoms, where we calculate the density matrix for the internal state of a sample of thermal atoms in a standing wave, and show how cooling processes can be simulated. Finally, we use the Monte Carlo wavefunction method to calculate the internal state of the atom, and compare the results and required computation time to those of the multi-level semiclassical technique.

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14

Bonacina, L., F. Casagrande, and A. Lulli. "Dynamics of a coherently driven micromaser by the Monte Carlo wavefunction approach." Journal of Optics B: Quantum and Semiclassical Optics 2, no. 4 (July 4, 2000): 490–96. http://dx.doi.org/10.1088/1464-4266/2/4/306.

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15

MURAMATSU, A., G. ZUMBACH, and X. ZOTOS. "A GEOMETRICAL VIEW OF THE MINUS-SIGN PROBLEM." International Journal of Modern Physics C 03, no. 01 (February 1992): 185–93. http://dx.doi.org/10.1142/s0129183192000154.

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Анотація:

It is shown that the sign of the fermionic determinant in the projector Monte Carlo method is directly related to a topological invariant. A key ingredient to obtain this result is the identification of the appropriate manifolds to describe the evolution of a fermionic trial wavefunction. They allow for a purely geometrical consideration of the minus-sign problem.

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16

Huggins, William J., Bryan A. O’Gorman, Nicholas C. Rubin, David R. Reichman, Ryan Babbush, and Joonho Lee. "Unbiasing fermionic quantum Monte Carlo with a quantum computer." Nature 603, no. 7901 (March 16, 2022): 416–20. http://dx.doi.org/10.1038/s41586-021-04351-z.

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AbstractInteracting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems1–4. Fermionic quantum Monte Carlo (QMC) methods5,6, which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver7,8, our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.

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17

TRIVEDI, NANDINI, and J. K. JAIN. "NUMERICAL STUDY OF JASTROW-SLATER TRIAL STATES FOR THE FRACTIONAL QUANTUM HALL EFFECT." Modern Physics Letters B 05, no. 07 (March 20, 1991): 503–10. http://dx.doi.org/10.1142/s0217984991000599.

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Анотація:

We study the recently proposed trial states for the fractional quantum Hall effect, which are constructed by multiplying the wavefunction for filled Landau levels with Jastrow correlation factors. In spite of the essential use of higher Landau levels, we demonstrate the validity of the variational states using Monte Carlo methods by showing that the Jastrow factors ensure (i) these states lie predominantly in the lowest Landau level and (ii) they have very low interaction energies.

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18

Zhou, Xiaojun, and Fan Wang. "Singlet–triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater–Jastrow trial wavefunction with a minimum number of determinants." Physical Chemistry Chemical Physics 21, no. 36 (2019): 20422–31. http://dx.doi.org/10.1039/c9cp03045j.

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19

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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Анотація:

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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20

Wolfseder, Brigitte, and Wolfgang Domcke. "Multi-mode vibronic coupling with dissipation. Application of the Monte Carlo wavefunction propagation method." Chemical Physics Letters 235, no. 3-4 (March 1995): 370–76. http://dx.doi.org/10.1016/0009-2614(95)00134-p.

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21

Ohta, S., M. Nakano, R. Kishi, H. Takahashi, and S. Furukawa. "Monte Carlo wavefunction approach to the exciton dynamics of molecular aggregates with exciton–phonon coupling." Chemical Physics Letters 419, no. 1-3 (February 2006): 70–74. http://dx.doi.org/10.1016/j.cplett.2005.11.052.

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22

Medhi, Amal, Saurabh Basu, and C. Y. Kadolkar. "Stability of the Gutzwiller projected BCS wavefunction in t–J bilayers: A variational Monte Carlo study." Physica C: Superconductivity 451, no. 1 (January 2007): 13–18. http://dx.doi.org/10.1016/j.physc.2006.09.010.

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23

Nakano, M., S. Ohta, R. Kishi, H. Takahashi, and S. Furukawa. "Monte Carlo wavefunction approach to the dissipative quantum-phase dynamics of two-component Bose-Einstein condensates." European Physical Journal D 38, no. 3 (March 14, 2006): 523–32. http://dx.doi.org/10.1140/epjd/e2006-00049-7.

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24

Arisue, Hiroaki. "Monte Carlo measurement of the vacuum wavefunction for non-abelian gauge theory in D=3 dimensions." Physics Letters B 280, no. 1-2 (April 1992): 85–90. http://dx.doi.org/10.1016/0370-2693(92)90777-2.

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25

Yanagisawa, T., M. Miyazaki, and K. Yamaji. "Strongly correlated superconductivity." International Journal of Modern Physics B 32, no. 17 (July 9, 2018): 1840023. http://dx.doi.org/10.1142/s0217979218400234.

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Анотація:

We investigate the electronic properties of the ground state of strongly correlated electron systems. We use an optimization variational Monte Carlo method for the two-dimensional Hubbard model and the three-band d-p model. The many-body wavefunction is improved and optimized by introducing variational parameters that control the correlation between electrons. The on-site repulsive Coulomb interaction U induces strong antiferromagnetic (AF) correlation. There is a crossover from weakly to strongly correlated regions as U increases. We show an idea that high-temperature superconductivity occurs as a result of this crossover in the strongly correlated region where U is greater than the bandwidth.

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26

MEIR, YIGAL. "A VARIATIONAL GROUND-STATE FOR THE ν=2/3 FRACTIONAL QUANTUM HALL REGIME". International Journal of Modern Physics B 10, № 12 (30 травня 1996): 1425–37. http://dx.doi.org/10.1142/s0217979296000544.

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Анотація:

A variational ν=2/3 state, which unifies the sharp edge picture of MacDonald with the soft edge picture of Chang and of Beenakker is presented and studied in detail. Using an exact relation between correlation functions of this state and those of the Laughlin ν=1/3 wavefunction, the correlation functions of the ν=2/3 state are determined via a classical Monte Carlo calculation, for systems up to 50 electrons. It is found that as a function of the slope of the confining potential there is a sharp transition of the ground state from one description to the other. This transition should be observable in tunneling experiments through quantum dots.

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27

Delle Site, Luigi. "Levy–Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo." Chemical Physics Letters 619 (January 2015): 148–51. http://dx.doi.org/10.1016/j.cplett.2014.11.060.

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28

Mancini, John S., and Joel M. Bowman. "Communication: A new ab initio potential energy surface for HCl–H2O, diffusion Monte Carlo calculations of D0 and a delocalized zero-point wavefunction." Journal of Chemical Physics 138, no. 12 (March 28, 2013): 121102. http://dx.doi.org/10.1063/1.4799231.

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29

Hastings, Matthew B. "Obstructions to classically simulating the quantum adiabatic algorithm." Quantum Information and Computation 13, no. 11&12 (November 2013): 1038–76. http://dx.doi.org/10.26421/qic13.11-12-8.

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Анотація:

We consider the adiabatic quantum algorithm for systems with ``no sign problem", such as the transverse field Ising model, and analyze the equilibration time for quantum Monte Carlo (QMC) on these systems. We ask: if the spectral gap is only inverse polynomially small, will equilibration methods based on slowly changing the Hamiltonian parameters in the QMC simulation succeed in a polynomial time? We show that this is {\it not} true, by constructing counter-examples. In some examples, the space of configurations where the wavefunction has non-negligible amplitude has a nontrivial fundamental group, causing the space of trajectories in imaginary time to break into disconnected components with only negligible probability outside these components. For the simplest example we give with an abelian fundamental group, QMC does not equilibrate but still solves the optimization problem. More severe effects leading to failure to solve the optimization can occur when the fundamental group is a free group on two generators. Other examples where QMC fails have a {\it trivial} fundamental group, but still use ideas from topology relating group presentations to simplicial complexes. We define gadgets to realize these Hamiltonians as the effective low-energy dynamics of a transverse field Ising model. We present some analytic results on equilibration times which may be of some independent interest in the theory of equilibration of Markov chains. Conversely, we show that a small spectral gap implies slow equilibration at low temperature for some initial conditions and for a natural choice of local QMC updates.

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30

Mølmer, Klaus, and Yvan Castin. "Monte Carlo wavefunctions in quantum optics." Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, no. 1 (February 1996): 49–72. http://dx.doi.org/10.1088/1355-5111/8/1/007.

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31

Wang, Ting, Xiaojun Zhou, and Fan Wang. "Performance of the Diffusion Quantum Monte Carlo Method with a Single-Slater-Jastrow Trial Wavefunction Using Natural Orbitals and Density Functional Theory Orbitals on Atomization Energies of the Gaussian-2 Set." Journal of Physical Chemistry A 123, no. 17 (April 5, 2019): 3809–17. http://dx.doi.org/10.1021/acs.jpca.9b01933.

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32

Bueckert, Hartmut, Stuart M. Rothstein, and Jan Vrbik. "Optimization of quantum Monte Carlo wavefunctions using analytical derivatives." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 366–71. http://dx.doi.org/10.1139/v92-052.

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Анотація:

We show how to optimize many-parameter wavefunctions for use in quantum Monte Carlo by deriving and utilizing formulas for analytical rather than numerical evaluation of the required derivatives. We present these in a form which is easily vectorizable for use on a supercomputer. We also discuss several technical issues of variational Monte Carlo to ensure both an unbiased and efficient optimization. Finally, we illustrate our optimization scheme's numerical performance by optimizing ground-state wavefunctions for LiH and H2O, each with more than 100 variational parameters. Keywords: quantum Monte Carlo, optimization, electron correlation, LiH, H2O.

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33

Alexander, S. A., and R. L. Coldwell. "Visualizing molecular wavefunctions using Monte Carlo methods." International Journal of Quantum Chemistry 109, no. 3 (2009): 385–400. http://dx.doi.org/10.1002/qua.21774.

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34

Scemama, Anthony, Thomas Applencourt, Emmanuel Giner, and Michel Caffarel. "Quantum Monte Carlo with very large multideterminant wavefunctions." Journal of Computational Chemistry 37, no. 20 (June 14, 2016): 1866–75. http://dx.doi.org/10.1002/jcc.24382.

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35

Per, Manolo C., and Deidre M. Cleland. "Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo." Journal of Chemical Physics 146, no. 16 (April 28, 2017): 164101. http://dx.doi.org/10.1063/1.4981527.

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36

Bouabça, Thomas, Benoît Braïda, and Michel Caffarel. "Multi-Jastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo." Journal of Chemical Physics 133, no. 4 (July 28, 2010): 044111. http://dx.doi.org/10.1063/1.3457364.

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37

Acioli, Paulo H., L. S. Costa, and Frederico V. Prudente. "Quantum Monte Carlo study of rovibrational states utilizing rotating wavefunctions: Application to H2O." Journal of Chemical Physics 111, no. 14 (October 8, 1999): 6311–15. http://dx.doi.org/10.1063/1.479935.

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38

Sabzevari, Iliya, Ankit Mahajan, and Sandeep Sharma. "An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo." Journal of Chemical Physics 152, no. 2 (January 14, 2020): 024111. http://dx.doi.org/10.1063/1.5125803.

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39

Zhang, Feng, Zhuo Ye, Yong-Xin Yao, Cai-Zhuang Wang, and Kai-Ming Ho. "A random-sampling method as an efficient alternative to variational Monte Carlo for solving Gutzwiller wavefunctions." Journal of Physics Communications 5, no. 12 (December 1, 2021): 125003. http://dx.doi.org/10.1088/2399-6528/ac3c32.

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Анотація:

Abstract We present a random-sampling (RS) method for evaluating expectation values of physical quantities using the variational approach. We demonstrate that the RS method is computationally more efficient than the variational Monte Carlo method using the Gutzwiller wavefunctions applied on single-band Hubbard models as an example. Non-local constraints can also been easily implemented in the current scheme that capture the essential physics in the limit of strong on-site repulsion. In addition, we extend the RS method to study the antiferromagnetic states with multiple variational parameters for 1D and 2D Hubbard models.

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40

Milotti, Edoardo, Sergio Bartalucci, Sergio Bertolucci, Massimiliano Bazzi, Mario Bragadireanu, Michael Cargnelli, Alberto Clozza, et al. "Semi-Analytical Monte Carlo Method to Simulate the Signal of the VIP-2 Experiment." Symmetry 13, no. 1 (December 22, 2020): 6. http://dx.doi.org/10.3390/sym13010006.

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The VIP-2 collaboration runs an apparatus in the Gran Sasso underground laboratories of the Italian Institute for Nuclear Physics (INFN) designed to search for anomalous X-rays from electron-atom interactions due to violations of the fundamental antisymmetry of multi-electron wavefunctions. The experiment implements the scheme first proposed by Ramberg and Snow, where a current source injects electrons into a metal strip (the experiment’s target). In this paper we describe the structure of a Monte Carlo program to simulate a new upgrade of the experiment, where the anomalous X-ray emission is modulated by an arbitrary time-varying input current. A novel feature of the simulation algorithm is that the Monte Carlo program is based on a mixture of analytical and numerical methods. We report preliminary, exploratory results on the expected detection rate for different modulations of the injected current; these results are a starting point on the way to optimize the modulation scheme and indicate a large potential improvement of the detection sensitivity.

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41

Kelsall, R. W. "Monte Carlo Simulations of Intersubband Hole Relaxation in a GaAs/AlAs Quantum Well." VLSI Design 8, no. 1-4 (January 1, 1998): 367–73. http://dx.doi.org/10.1155/1998/87925.

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An ensemble Monte Carlo code has been developed for the simulation of hole relaxation processes in a GaAs/AlAs quantum well. The code includes a realistic k.p model of the valence subbands and corresponding wavefunctions. Intra- and inter-subband phonon scattering rates are calculated for polar and non-polar interactions via both optical and acoustic modes. The code is used to simulate the cooling of non-equilibrium photogenerated hole populations. A lifetime of 90 fs is extracted for optical phonon mediated depopulation of the 4th subband at 77K. By contrast, the 2nd subband exhibits fast re-population, but slow de-population, with extracted lifetimes of up to 160 ps. The slow depopulation is attributed to the small energy separation of the 1st and 2nd subbands (less than the optical phonon energy) and the large density of states in the 2nd subband off-zone-centre minimum.

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42

Bressanini, Dario, Massimo Mella, and Gabriele Morosi. "Many-electron correlated exponential wavefunctions. A quantum Monte Carlo application to H2 and He2+." Chemical Physics Letters 240, no. 5-6 (July 1995): 566–70. http://dx.doi.org/10.1016/0009-2614(95)00561-h.

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43

Morf, R., and B. I. Halperin. "Monte Carlo evaluation of trial wavefunctions for the fractional quantized Hall effect: Spherical geometry." Zeitschrift f�r Physik B Condensed Matter 68, no. 2-3 (June 1987): 391–406. http://dx.doi.org/10.1007/bf01304256.

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44

Greensite, J., and J. Iwasaki. "Monte Carlo study of the Yang-Mills vacuum wavefunctional in D=4 dimensions." Physics Letters B 223, no. 2 (June 1989): 207–12. http://dx.doi.org/10.1016/0370-2693(89)90240-2.

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45

Kohno, Masanori, and Masatoshi Imada. "Systematic improvement of wavefunctions in the variational Monte Carlo method for the t–J model." Journal of Physics and Chemistry of Solids 63, no. 6-8 (June 2002): 1563–66. http://dx.doi.org/10.1016/s0022-3697(02)00047-1.

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46

Juillet, Olivier, Alexandre Leprévost, Jérémy Bonnard, and Raymond Frésard. "Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree–Fock–Bogoliubov wavefunctions." Journal of Physics A: Mathematical and Theoretical 50, no. 17 (March 29, 2017): 175001. http://dx.doi.org/10.1088/1751-8121/aa62b6.

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47

PREDESCU, CRISTIAN. "SPATIALLY-DISCRETIZED HIGH-TEMPERATURE APPROXIMATIONS AND THEIR O(N) IMPLEMENTATION ON A GRID." Journal of Theoretical and Computational Chemistry 05, no. 02 (June 2006): 255–80. http://dx.doi.org/10.1142/s0219633606002246.

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We consider the problem of performing imaginary-time propagation of wavefunctions on a grid. We demonstrate that spatially-continuous high-temperature approximations can be discretized in such a way that their convergence order is preserved. Requirements of minimal computational work and reutilization of data then uniquely determine the optimal grid, quadrature technique, and propagation method. It is shown that the optimal propagation technique is O(N), with respect to the grid size. The grid technique is utilized to compare the Monte Carlo efficiency of the Trotter–Suzuki approximation against a recently introduced fourth-order high-temperature approximation, while circumventing the issue of statistical noise, which usually prevents such comparisons from being carried out. We document the appearance of a systematic bias in the Monte Carlo estimators that involve temperature differentiation of the density matrix, bias that is due to the dependence of the eigenvalues on the inverse temperature. This bias is negotiated more successfully by the short-time approximations having higher convergence order, which leads to non-trivial computational savings.

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48

Peng, Yun, Xiaojun Zhou, Zhifan Wang, and Fan Wang. "Diffusion Monte Carlo method on small boron clusters using single- and multi- determinant–Jastrow trial wavefunctions." Journal of Chemical Physics 154, no. 2 (January 14, 2021): 024301. http://dx.doi.org/10.1063/5.0031051.

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49

Bertini, Luca, Massimo Mella, Dario Bressanini, and Gabriele Morosi. "Explicitly correlated trial wavefunctions in quantum Monte Carlo calculations of excited states of Be and Be-." Journal of Physics B: Atomic, Molecular and Optical Physics 34, no. 3 (January 18, 2001): 257–66. http://dx.doi.org/10.1088/0953-4075/34/3/304.

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50

Clay, Raymond C., and Miguel A. Morales. "Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo." Journal of Chemical Physics 142, no. 23 (June 16, 2015): 234103. http://dx.doi.org/10.1063/1.4921984.

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