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.
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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.