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
-
A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations
Jin, Shi | Li, XiantaoCommunications on Applied Mathematics and Computation, Vol. (2023), Iss.
https://doi.org/10.1007/s42967-023-00336-z [Citations: 0] -
Random-batch list algorithm for short-range molecular dynamics simulations
Liang, Jiuyang | Xu, Zhenli | Zhao, YueThe Journal of Chemical Physics, Vol. 155 (2021), Iss. 4
https://doi.org/10.1063/5.0056515 [Citations: 7] -
A random batch method for efficient ensemble forecasts of multiscale turbulent systems
Qi, Di | Liu, Jian-GuoChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 33 (2023), Iss. 2
https://doi.org/10.1063/5.0129127 [Citations: 2] -
Stochastic algorithms for self-consistent calculations of electronic structures
Ko, Taehee | Li, XiantaoMathematics of Computation, Vol. 92 (2023), Iss. 342 P.1693
https://doi.org/10.1090/mcom/3826 [Citations: 1] -
Intrinsic statistical regularity of topological charges revealed in dynamical disk model
Sun, Ranzhi | Yao, ZhenweiPhysical Review E, Vol. 110 (2024), Iss. 3
https://doi.org/10.1103/PhysRevE.110.035302 [Citations: 0] -
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] -
On the Random Batch Method for Second Order Interacting Particle Systems
Jin, Shi | Li, Lei | Sun, YiqunMultiscale Modeling & Simulation, Vol. 20 (2022), Iss. 2 P.741
https://doi.org/10.1137/20M1383069 [Citations: 4] -
Active Particles, Volume 3
Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings
Jin, Shi | Li, Lei2022
https://doi.org/10.1007/978-3-030-93302-9_5 [Citations: 3]