Hellmann and Feynman theorem versus diffusion Monte Carlo experiment

TL;DR

This paper introduces a new estimator method based on the Hellmann-Feynman theorem for diffusion Monte Carlo simulations, addressing bias issues in measuring non-commuting observables.

Contribution

It proposes a novel direct approach to estimate observables that do not commute with the Hamiltonian, reducing bias in diffusion Monte Carlo calculations.

Findings

New estimator reduces bias in DMC measurements

Applied to measure radial distribution function of Fermion fluid

Demonstrates effectiveness of the Hellmann-Feynman based approach

Abstract

In a computer experiment the choice of suitable estimators to measure a physical quantity plays an important role. We propose a new direct route to determine estimators for observables which do not commute with the Hamiltonian. Our new route makes use of the Hellmann and Feynman theorem and in a diffusion Monte Carlo simulation it introduces a new bias to the measure due to the choice of the auxiliary function. This bias is independent from the usual one due to the choice of the trial wave function. We used our route to measure the radial distribution function of a spin one half Fermion fluid.