Massless Schwinger model with a 4-fermi interaction at topological angle $\theta = \pi$

TL;DR

This paper investigates the phase structure of the massless Schwinger model with a 4-fermi interaction at topological angle $ heta = \pi$, revealing a critical point where charge conjugation symmetry is spontaneously broken.

Contribution

It introduces a lattice formulation with staggered fermions and a worldline/worldsheet representation to study charge conjugation symmetry breaking at $ heta = \pi$ in this model.

Findings

Identifies a critical point separating symmetric and broken phases.

Demonstrates the effectiveness of the worldline/worldsheet approach in overcoming the complex action problem.

Shows spontaneous charge conjugation symmetry breaking at strong coupling.

Abstract

We study the massless Schwinger model with an additional 4-fermi interaction and a topological term. For topological angle $\theta = \pi$ charge conjugation symmetry is implemented in a non-trivial way and we study the possibility of its spontaneous breaking. For the lattice discretization we use staggered fermions and the Villain action for the gauge fields, where the topological term is an integer and charge conjugation at $\theta = \pi$ is an exact symmetry. The complex action problem is overcome by a suitable worldline/worldsheet representation. We find that as a function of the 4-fermi coupling the system shows a critical point separating a weak coupling phase where charge conjugation symmetry is intact from a strong coupling phase with spontaneously broken charge conjugation symmetry.