Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model

TL;DR

This study uses diffusion Monte Carlo simulations to analyze the radial distribution function of a spin-one-half fermion fluid with tunable interactions, highlighting estimator choices and biases in computational measurements.

Contribution

It introduces and compares estimators for the radial distribution function in fermion fluids, including a new bias analysis due to an auxiliary function in DMC simulations.

Findings

Radial distribution functions vary with density, interaction parameter, and polarization.

The Hellmann-Feynman estimator introduces a bias independent of trial wave function choice.

Choice of estimator significantly affects the accuracy of physical quantity measurements.

Abstract

We study, through the diffusion Monte Carlo method, a spin one-half fermion fluid, in the three dimensional Euclidean space, at zero temperature. The point particles, immersed in a uniform "neutralizing" background, interact with a pair-potential which can be continuously changed from zero to the Coulomb potential depending on a parameter $\mu$. We determine the radial distribution functions of the system for various values of density, $\mu$, and polarization. We discuss about the importance, in a computer experiment, of the choice of suitable estimators to measure a physical quantity. The radial distribution function is determined through the usual histrogram estimator and through an estimator determined via the use of the Hellmann and Feynman theorem. In a diffusion Monte Carlo simulation the latter route introduces a new bias to the measure of the radial distribution function 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. A brief account of the results from this study were presented in a recent communication [R. Fantoni, Solid State Communications, {\bf 159}, 106 (2013)].