Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations

TL;DR

This paper introduces a multilevel blocking algorithm that effectively mitigates the fermion sign problem in finite-temperature quantum Monte Carlo simulations, demonstrated on interacting electrons in a quantum dot.

Contribution

The paper presents a novel recursive multilevel blocking method that improves sign cancellation in fermionic path integral Monte Carlo simulations.

Findings

Effective reduction of the fermion sign problem demonstrated

Applicable to systems with nearest-neighbor interactions in Trotter direction

Validated on interacting electrons in a quantum dot

Abstract

A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter direction. This multilevel approach systematically implements a simple blocking strategy in a recursive manner to synthesize the sign cancellations among different fermionic paths throughout the whole configuration space. The practical usefulness of the method is demonstrated for interacting electrons in a quantum dot.