Reweighting twisted boundary conditions

TL;DR

This paper investigates reweighting twisted boundary conditions in lattice QCD to restore unitarity, demonstrating its effectiveness especially in small volumes and for large twisting angles, with measurable impacts on physical observables.

Contribution

It introduces a reweighting method to include twisted boundary conditions in gauge averages, avoiding the need for new configurations and restoring unitarity in lattice simulations.

Findings

Reweighting effects are negligible in large volumes.

Significant effects observed in small volumes with large twisting angles.

Measurable shifts in plaquette and pion correlation functions.

Abstract

Imposing twisted boundary conditions on the fermionic fields is a procedure extensively used when evaluating, for example, form factors on the lattice. Twisting is usually performed for one flavour and only in the valence, and this causes a breaking of unitarity. In this work we explore the possibility of restoring unitarity through the reweighting method. We first study some properties of the approach at tree level and then we stochastically evaluate ratios of fermionic determinants for different boundary conditions in order to include them in the gauge averages, avoiding in this way the expensive generation of new configurations for each choice of the twisting angle, $\theta$. As expected the effect of reweighting is negligible in the case of large volumes but it is important when the volumes are small and the twisting angles are large. In particular we find a measurable effect for the plaquette and the pion correlation function in the case of $\theta=\pi/2$ in a volume $16\times 8^3$, and we observe a systematic upward shift in the pion dispersion relation.