Unexpected Results in the Chiral Limit with Staggered Fermions

TL;DR

This paper introduces a new cluster algorithm with a loop representation to study the chiral limit in lattice Schwinger models with staggered fermions, revealing unexpected mass generation for mesons at finite lattice spacings.

Contribution

It develops a novel loop-based cluster algorithm for the strongly coupled lattice Schwinger model with staggered fermions, providing new insights into meson masses in the chiral limit.

Findings

No long-range correlations at strong couplings.

All mesons acquire mass at non-zero lattice spacings.

Results challenge typical expectations of a massless pion in staggered fermions.

Abstract

A cluster algorithm is constructed and applied to study the chiral limit of the strongly coupled lattice Schwinger model involving staggered fermions. The algorithm is based on a novel loop representation of the model. Finite size scaling of the chiral susceptibility based on data from lattices of size up to $64\times 64$ indicates the absence of long range correlations at strong couplings. Assuming that there is no phase transition at a weaker coupling, the results imply that all mesons acquire a mass at non-zero lattice spacings. Although this does not violate any known physics, it is surprising since typically one expects a single pion to remain massless at non-zero lattice spacings in the staggered fermion formulation.