Unbiased estimators in Quantum Monte Carlo methods: application to liquid $^4$He

TL;DR

This paper introduces an unbiased Monte Carlo algorithm for quantum expectation values that improves accuracy and stability in many-body systems, demonstrated on hydrogen and liquid helium-4.

Contribution

It presents a new unbiased estimator algorithm for quantum Monte Carlo that integrates seamlessly with Green's Function methods without requiring side walks.

Findings

Accurately computes expectation values for hydrogen atom and molecule.

Achieves excellent results for liquid $^4$He at zero temperature.

Demonstrates stability and unbiasedness of the method.

Abstract

A Monte Carlo algorithm for computing quantum mechanical expectation values of coordinate operators in many body problems is presented. The algorithm, that relies on the forward walking method, fits naturally in a Green's Function Monte Carlo calculation, i.e., it does not require side walks or a bilinear sampling method. Our method evidences stability regions large enough to accurately sample unbiased pure expectation values. The proposed algorithm yields accurate results when it is applied to test problems as the hydrogen atom and the hydrogen molecule. An excellent description of several properties of a fully many body problem as liquid $^4$He at zero temperature is achieved.