Is Schwinger Model at Finite Density a Crystal?

TL;DR

This paper challenges the traditional view that the Schwinger model at finite density forms a crystal, showing that previous inhomogeneities are due to unphysical assumptions and that a true crystal formation requires heavy neutral particles to organize into a lattice.

Contribution

It demonstrates that the observed inhomogeneity in the Schwinger model is an artifact of explicit translational symmetry breaking and explores conditions under which a crystal structure can form with dynamical particles.

Findings

Inhomogeneity arises from unphysical background charge assumptions.

Heavy neutral particles can form a crystal at high density.

Standard FKS picture of oscillations is not valid with dynamical backgrounds.

Abstract

It has been believed since the paper by Fischler, Kogut and Susskind (FKS) that in QED_2 at finite charge density the chiral condensate exhibits a spatially inhomogeneous, oscillating behaviour. In this paper we demonstrate that this inhomogeneity is due to unphysical explicit breaking of the translational invariance by a uniform background charge density. Moreover, we investigate in the context of a simple statistical model what happens if the neutralizing background is composed instead of heavy, but dynamical, particles. We find that in contrast to the standard picture of FKS, the chiral condensate will not exhibit coherent oscillations on large distance scales, unless the heavy neutralizing particles themselves form a crystal and the density is high.