Chiral Limit of Strongly Coupled Lattice Gauge Theories

TL;DR

This paper introduces an efficient cluster algorithm for strongly coupled U(N) lattice gauge theories with staggered fermions, revealing non-zero chiral condensates in 3D and 4D and correcting previous misconceptions caused by autocorrelation issues.

Contribution

The authors develop a novel cluster algorithm based on the monomer-dimer representation, enabling more accurate analysis of the chiral limit in strongly coupled gauge theories.

Findings

Non-zero chiral condensate in 3D and 4D

Finite-size scaling of chiral correlations with specific exponent

Previous results were affected by autocorrelation problems

Abstract

We construct a new and efficient cluster algorithm for updating strongly coupled U(N) lattice gauge theories with staggered fermions in the chiral limit. The algorithm uses the constrained monomer-dimer representation of the theory and should also be of interest to researchers working on other models with similar constraints. Using the new algorithm we address questions related to the chiral limit of strongly coupled U(N) gauge theories beyond the mean field approximation. We show that the infinite volume chiral condensate is non-zero in three and four dimensions. However, on a square lattice of size $L$ we find $\sum_x < \bar\psi\psi(x) \bar\psi\psi(0) > \sim L^{2-\eta}$ for large $L$ where $\eta = 0.420(3)/N + 0.078(4)/N^2$. These results differ from an earlier conclusion obtained using a different algorithm. Here we argue that the earlier calculations were misleading due to uncontrolled autocorrelation times encountered by the previous algorithm.