Permutation blocking path integral Monte Carlo: A highly efficient approach to the simulation of strongly degenerate non-ideal fermions

TL;DR

This paper introduces a highly efficient permutation blocking path integral Monte Carlo method that significantly alleviates the fermion sign problem, enabling accurate simulations of strongly degenerate non-ideal fermions at low temperatures.

Contribution

The authors develop a novel PIMC approach combining a fourth-order density matrix factorization with antisymmetric propagators and an adapted worm algorithm, improving sampling efficiency and permutation blocking.

Findings

Achieves accurate simulations for up to 20 electrons at low temperature.

Effectively reduces the fermion sign problem through permutation blocking.

Provides benchmark results for strongly degenerate fermions where previous methods failed.

Abstract

Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices. To efficiently run through the modified configuration space, we introduce a modification of the widely used continuous space worm algorithm, which allows for an efficient sampling at arbitrary system parameters. We demonstrate how the application of determinants achieves an effective blocking of permutations with opposite signs, leading to a significant relieve of the fermion sign problem. To benchmark the capability of our method regarding the simulation of degenerate fermions, we consider multiple electrons in a quantum dot and compare our results with other ab initio techniques, where they are available. The present permutation blocking path integral Monte Carlo approach allows us to obtain accurate results even for $N=20$ electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.