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An efficient sampling algorithm for Variational Monte Carlo

Anthony Scemama·Tony Lelièvre·Gabriel Stoltz·Eric Cancès·Michel Caffarel
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Abstract

We propose a new algorithm for sampling the $N$-body density $|Ψ({\bf R})|^2/\int_{\mathbb{R}^{3N}} |Ψ|^2$ in the Variational Monte Carlo (VMC) framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space $({\bf R},{\bf P})$ improved by a Metropolis acceptation/rejection step. We show through some representative numerical examples (Lithium, Fluorine and Copper atoms, and phenol molecule), that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).

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Anthony Scemama, Tony Lelièvre, Gabriel Stoltz, Eric Cancès, Michel Caffarel. 2006-06-16. An efficient sampling algorithm for Variational Monte Carlo. https://doi.org/10.1063/1.2354490

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