Local Coarse-grained Approximation to Path Integral Monte Carlo Integration for Fermion Systems

TL;DR

This paper introduces a coarse-grained approximation method for path integral Monte Carlo simulations of fermions, reducing sign fluctuations and preventing collapse into bosonic states at low temperatures.

Contribution

It proposes a novel coarse-grained approximation technique for exchange effects in fermionic path integral Monte Carlo simulations, improving stability and accuracy.

Findings

Reduces sign fluctuations in fermion simulations

Prevents fermion system collapse into bosons at low temperatures

Proven to be exact for free particles

Abstract

An approximate treatment of exchange in finite-temperature path integral Monte Carlo simulations for fermions has been proposed. In this method, some of the fine details of density matrix due to permutations have been smoothed over or averaged out by using the coarse-grained approximation. The practical usefulness of the method is tested for interacting fermions in a three dimensional harmonic well. The results show that, the present method not only reduces the sign fluctuation of the density matrix, but also avoid the fermion system collapsing into boson system at low temperatures. The method is substantiated to be exact when applied to free particles.