Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions

TL;DR

This paper investigates the sign problem in strongly coupled lattice QED with Wilson fermions using the fermion bag approach, identifying classes of fermion bags and proposing a simplified model with reduced or no sign problem.

Contribution

The study introduces a fermion bag formulation for lattice QED, classifies fermion bags, and proposes a modified partition function to mitigate the sign problem.

Findings

Complex fermion bags have nearly equal positive and negative weights, causing a severe sign problem.

Simple fermion bags mostly have positive weights, and their dominance suggests a possible approximation.

A simplified model without sign problems is identified, especially at large hopping parameters.

Abstract

We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and this leads to a severe sign problem. On the other hand simple bags mostly have a positive weight. Since the complex bags almost cancel each other, we suggest that eliminating them from the partition function may be a good approximation. This modified partition function suffers only from a mild sign problem. We also find a simpler model which does not suffer from any sign problem and may still be a good approximation at small and intermediate values of the hopping parameter. We also prove that when the hopping parameter is strictly infinite all fermion bags are non-negative.