The fermion sign problem: A new decoupling transformation, and a new simulation algorithm

TL;DR

This paper introduces a new transformation and algorithm for studying fermionic systems that provides detailed sign information and efficiently covers various densities and interaction strengths, aligning well with exact results.

Contribution

It proposes a novel transformation that reveals sign information and a versatile algorithm for simulating a wide parameter range in fermionic models.

Findings

Transformation clearly distinguishes positive and negative sign configurations.

Algorithm efficiently computes results across different densities and interaction strengths.

Results agree closely with exact calculations.

Abstract

We discuss the Fermion sign problem and, by examining a very general Hubbard-Stratonovich (HS) transformation, argue that the sign problem cannot be solved with such methods. We propose a different kind of transformation which, while not solving the sign problem, shows more detailed information about the system. With our transformation it is {\it trivial} to tell which auxiliary field configurations give a positive sign and which give a negative sign. We then discuss briefly various properties of this transformation and construct a new algorithm which with one simulation gives results for a whole range of particle densities and Hubbard $U$ values, positive and negative. Our approach is in excellent agreement with exact calculations.