# The Phase Structure of the Schwinger Model on the Lattice with Wilson Fermions in the Hartree-Fock Approximation

## TL;DR

This paper explores the phase diagram of the lattice Schwinger model with Wilson fermions using the Hartree-Fock approximation, revealing parity and flavor symmetry breaking at various couplings.

## Contribution

It provides a novel Hartree-Fock analysis of the Schwinger model's phase structure with Wilson fermions, including predictions of symmetry breaking phenomena.

## Key findings

- Parity violating phase at weak and intermediate couplings for one flavor
- Spontaneous parity and flavor breaking at strong coupling with two flavors
- Nonzero electric field in the broken phase

## Abstract

The phase diagram of the Schwinger model on the lattice with one and two degenerate flavours of Wilson fermions is investigated in the Hartree-Fock approximation. In case of a single flavour (not directly amenable to numerical simulation), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. In the broken phase, the Hartree-Fock vacuum sustains a nonzero electric field. With two flavours, parity is not broken at weak coupling. However, both parity and flavour become spontaneously broken at the Hartree-Fock level as the coupling becomes strong.