Perturbative Removal of a Sign Problem

TL;DR

This paper introduces an exact, systematic method leveraging perturbation theory to significantly reduce the sign problem in lattice path integrals, demonstrated on the Thirring model.

Contribution

The paper presents a novel, exact approach that uses systematic expansion to alleviate the sign problem without approximation, and is systematically improvable.

Findings

Successfully reduces the sign problem in the Thirring model

Method is exact and systematically improvable

Demonstrates effectiveness in finite-density lattice systems

Abstract

This paper presents a method for alleviating sign problems in lattice path integrals, including those associated with finite fermion density in relativistic systems. The method makes use of information gained from some systematic expansion -- such as perturbation theory -- in order to accelerate the Monte Carlo. The method is exact, in the sense that no approximation to the lattice path integral is introduced. Thanks to the underlying systematic expansion, the method is systematically improvable, so that an arbitrary reduction in the sign problem can in principle be obtained. The Thirring model (in 0 + 1 and 1 + 1 dimensions) is used to demonstrate the ability of this method to reduce the finite-density sign problem.