Random Batch Algorithms for Quantum Monte Carlo Simulations

Random Batch Algorithms for Quantum Monte Carlo Simulations

Year:    2020

Author:    Shi Jin, Xiantao Li

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1907–1936

Abstract

Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the potential energy, and the two-body terms in the Jastrow factor. In the framework of variational Monte Carlo methods, the random batch algorithm is constructed based on the over-damped Langevin dynamics, so that updating the position of each particle in an $N$-particle system only requires $\mathcal{O}(1)$ operations, thus for each time step the computational cost for $N$ particles is reduced from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. For diffusion Monte Carlo methods, the random batch algorithm uses an energy decomposition to avoid the computation of the total energy in the branching step. The effectiveness of the random batch method is demonstrated using a system of liquid $^4$He atoms interacting with a graphite surface.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0168

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1907–1936

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Quantum Monte Carlo method random batch methods Langevin equation.

Author Details

Shi Jin

Xiantao Li

  1. A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations

    Jin, Shi | Li, Xiantao

    Communications on Applied Mathematics and Computation, Vol. (2023), Iss.

    https://doi.org/10.1007/s42967-023-00336-z [Citations: 0]
  2. Random-batch list algorithm for short-range molecular dynamics simulations

    Liang, Jiuyang | Xu, Zhenli | Zhao, Yue

    The Journal of Chemical Physics, Vol. 155 (2021), Iss. 4

    https://doi.org/10.1063/5.0056515 [Citations: 7]
  3. A random batch method for efficient ensemble forecasts of multiscale turbulent systems

    Qi, Di | Liu, Jian-Guo

    Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 33 (2023), Iss. 2

    https://doi.org/10.1063/5.0129127 [Citations: 2]
  4. Stochastic algorithms for self-consistent calculations of electronic structures

    Ko, Taehee | Li, Xiantao

    Mathematics of Computation, Vol. 92 (2023), Iss. 342 P.1693

    https://doi.org/10.1090/mcom/3826 [Citations: 1]
  5. Intrinsic statistical regularity of topological charges revealed in dynamical disk model

    Sun, Ranzhi | Yao, Zhenwei

    Physical Review E, Vol. 110 (2024), Iss. 3

    https://doi.org/10.1103/PhysRevE.110.035302 [Citations: 0]
  6. Asymptotic-preserving schemes for multiscale physical problems

    Jin, Shi

    Acta Numerica, Vol. 31 (2022), Iss. P.415

    https://doi.org/10.1017/S0962492922000010 [Citations: 30]
  7. On the Random Batch Method for Second Order Interacting Particle Systems

    Jin, Shi | Li, Lei | Sun, Yiqun

    Multiscale Modeling & Simulation, Vol. 20 (2022), Iss. 2 P.741

    https://doi.org/10.1137/20M1383069 [Citations: 4]
  8. Active Particles, Volume 3

    Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings

    Jin, Shi | Li, Lei

    2022

    https://doi.org/10.1007/978-3-030-93302-9_5 [Citations: 3]