Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions

TL;DR

This paper compares Monte Carlo energy and variance minimization methods for optimizing many-body wave functions, highlighting variance minimization's superior stability and proposing an efficient scheme for large systems.

Contribution

It introduces a robust variance minimization technique and analyzes the stability and characteristics of different Monte Carlo optimization methods for many-body wave functions.

Findings

Variance minimization shows better numerical stability than energy minimization.

A robust and efficient variance minimization scheme is identified for large systems.

The methods are validated using a 64-electron silicon model.

Abstract

We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in correlated sampling estimations of the energy and its variance. We investigate the numerical stability of the techniques and identify two reasons why variance minimization exhibits superior numerical stability to energy minimization. The characteristics of each method are studied using a non-interacting 64-electron model of crystalline silicon. While our main interest is in solid state systems, the issues investigated are relevant to Monte Carlo studies of atoms, molecules and solids. We identify a robust and efficient variance minimization scheme for optimizing wave functions for large systems.