Chiral Limit of Staggered Fermions at Strong Couplings: A Loop Representation

TL;DR

This paper introduces a loop-variable representation of two-dimensional staggered fermions at strong coupling, enabling a new algorithm to study chiral properties, but results are uncertain due to potential algorithm limitations.

Contribution

The paper develops a novel loop representation and a non-local Monte Carlo algorithm for analyzing chiral susceptibility in strongly coupled fermion-gauge systems.

Findings

Algorithm reproduces exact results on small lattices

Finds non-zero pion mass for all N, increasing with N

Results may be unreliable for large volumes due to algorithm breakdown

Abstract

The partition function of two dimensional massless staggered fermions interacting with U(N) gauge fields is rewritten in terms of loop variables in the strong coupling limit. We use this representation of the theory to devise a non-local Metropolis algorithm to calculate the chiral susceptibility. For small lattices our algorithm reproduces exact results quite accurately. Applying this algorithm to large volumes yields rather surprising results. In particular we find $m_\pi \neq 0$ for all $N$ and it increases with $N$. Since the talk was presented we have found reasons to believe that our algorithm breaks down for large volumes questioning the validity of our results.