On reweighting for twisted boundary conditions

TL;DR

This paper investigates reweighting techniques to correct unitarity breaking caused by twisted boundary conditions in lattice gauge theory simulations, analyzing their effectiveness and impact on physical observables.

Contribution

It introduces a factorization approach for fermionic reweighting determinants and evaluates its effectiveness across different volume sizes and twisting angles.

Findings

Reweighting effects are negligible in large volumes.

Reweighting has significant effects in small volumes with large twisting angles.

Twisting angles influence the critical quark mass and dispersion relation violations.

Abstract

We consider the possibility of using reweighting techniques in order to correct for the breaking of unitarity when twisted boundary conditions are imposed on valence fermions in simulations of lattice gauge theories. We start by studying the properties of reweighting factors and their variances at tree-level. That leads us to the introduction of a factorization for the fermionic reweighting determinant. In the numerical, stochastic, implementation of the method, we find that the effect of reweighting is negligible in the case of large volumes but it is sizeable when the volumes are small and the twisting angles are large. More importantly, we find that for un-improved Wilson fermions, and in small volumes, the dependence of the critical quark mass on the twisting angle is quite pronounced and results in large violations of the continuum dispersion relation.