The fermion bag approach to lattice field theories

TL;DR

The paper introduces the fermion bag approach to address the fermion sign problem in lattice field theories, providing a new computational framework that confines the sign problem to small regions called bags, improving efficiency in certain regimes.

Contribution

The paper proposes the fermion bag approach as a novel method to mitigate the fermion sign problem and demonstrates its effectiveness using the 3D massless lattice Thirring model.

Findings

Fermion bags are small and manageable in certain parameter regimes.

The approach yields accurate critical exponents for the quantum phase transition.

Provides insights and solutions to the sign problem and the silver blaze problem.

Abstract

We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$ becomes finite fermions are liberated but are naturally confined to regions which we refer to as {\em fermion bags}. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three dimensional massless lattice Thirring model as an example we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find $\nu=0.87(2)$ and $\eta=0.62(2)$.