Central Charge of the Parallelogram Lattice Strong Coupling Schwinger Model

TL;DR

This paper introduces a Fierzed hopping expansion for strong coupling Wilson fermions and demonstrates its application to the Schwinger model on parallelogram lattices, revealing connections to 6-vertex models and exploring richer systems.

Contribution

It presents a new Fierzed hopping expansion method for strong coupling fermions and applies it to analyze the Schwinger model on non-rectangular lattices, linking to exactly solvable models.

Findings

The strong coupling Schwinger model spans the $ ext{Delta}=-1$ critical line of 6-vertex models.

Fierzed formulation applies to backtracking Wilson fermions, indicating potential for richer systems.

Identified connections between lattice skewness and critical lines in vertex models.

Abstract

We put forth a Fierzed hopping expansion for strong coupling Wilson fermions. As an application, we show that the strong coupling Schwinger model on parallelogram lattices with nonbacktracking Wilson fermions span, as a function of the lattice skewness angle, the $\Delta = -1$ critical line of $6$-vertex models. This Fierzed formulation also applies to backtracking Wilson fermions, which as we describe apparently correspond to richer systems. However, we have not been able to identify them with exactly solved models.