Overcoming the fermion sign problem in homogeneous systems

TL;DR

This paper introduces a polynomial scaling algorithm for path integral Monte Carlo simulations of homogeneous fermionic systems, significantly reducing computational cost and overcoming the fermion sign problem.

Contribution

It demonstrates that exchange probabilities are independent of other permutations, enabling a simple model to generate the antisymmetrized density matrix efficiently.

Findings

Achieved up to 10 orders of magnitude increase in efficiency.

Developed a model based on exchange probabilities for 3-He and electron gas.

Provided a polynomial scaling method for fermionic PIMC simulations.

Abstract

Explicit treatment of many-body Fermi statistics in path integral Monte Carlo (PIMC) results in exponentially scaling computational cost due to the near cancellation of contributions to observables from even and odd permutations. Through direct analysis of exchange statistics we find that individual exchange probabilities in homogeneous systems are, except for finite size effects, independent of the configuration of other permutations present. For two representative systems, 3-He and the homogeneous electron gas, we show that this allows the entire antisymmetrized density matrix to be generated from a simple model depending on only a few parameters obtainable directly from a standard PIMC simulation. The result is a polynomial scaling algorithm and up to a 10 order of magnitude increase in efficiency in measuring fermionic observables for the systems considered.