# Surface modes and parity violation in Schwinger model on the lattice

## TL;DR

This paper explores the phase diagram of the lattice Schwinger model with Wilson fermions, revealing a parity-violating phase at various couplings through Hartree-Fock approximation analysis.

## Contribution

It provides the first Hartree-Fock based analysis of the lattice Schwinger model's phase structure, including parity violation and electric field behavior.

## Key findings

- Parity violating phase exists at weak and intermediate couplings
- Hartree-Fock vacuum sustains a nonzero electric field in the broken phase
- Phase structure with two flavors is also discussed

## Abstract

The phase diagram of the Schwinger model on the lattice with Wilson fermions is investigated in the Hartree-Fock approximation. In case of single flavour (not directly amenable to simulations), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. Hartree-Fock vacuum sustains a nonzero electric field in this broken phase. The phase structure of the model with two flavours is also discussed.

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Source: https://tomesphere.com/paper/hep-lat/9509089