Mitigating the sign problem for non-relativistic fermions on the lattice

TL;DR

This paper investigates the fermion sign problem in non-relativistic fermion theories, proposing a polar momentum space approach that may reduce the sign problem and enable more efficient low-energy calculations on the lattice.

Contribution

It introduces a polar momentum space formulation for non-relativistic fermions that potentially weakens the sign problem, facilitating low-energy lattice computations.

Findings

Sign problem appears weaker in the effective low-energy theory.

Modifications to the action can make the theory positive semi-definite.

A lattice realization of the polar momentum space approach is discussed.

Abstract

We study the fermion sign problem in a theory of non-relativistic fermions with a spin-independent repulsive interaction. We work in polar co-ordinates in momentum space, which makes it straightforward to keep only the low-energy degrees of freedom close to the Fermi surface. This is sufficient for the purpose of calculating many physically important low-energy observables. We find indications that the sign problem in this effective theory will be weaker than in the full theory, so low-energy properties of the theory could be calculated by modifying the action to make it positive semi-definite and including reweighting factors in the observables. We discuss suitable modifications of the action, and describe a possible lattice realization of the polar momentum space formulation of the theory.