The Schwinger and Thirring models at finite chemical potential and temperature

TL;DR

This paper analyzes the massless Schwinger and Thirring models at finite temperature and chemical potential, revealing a topological phase contribution and exact solutions for the generating functional, partition function, and propagators.

Contribution

It provides the first exact evaluation of the generating functional and partition function for these models at nonzero temperature and chemical potential, including topological effects.

Findings

Identified a topological phase induced by chemical potential.

Derived exact expressions for the generating functional and partition function.

Showed bosonization persists at finite T and  with unchanged mass.

Abstract

We study the generating functional for the massless Schwinger model in the torus, at nonzero chemical potential and temperature. The lack of hermiticity of the Dirac operator yields a non-trivial phase in the effective action, which is a topological contribution induced by the chemical potential. In the sector with no zero modes, we evaluate exactly the generating functional, the partition function, the boson propagator and the thermally averaged Polyakov loop. The system bosonizes at finite T and \mu, with the same mass as in vacuum. From the solution obtained for the Schwinger model we derive also exactly the generating functional and the partition function for the massless Thirring model at nonzero T and \mu.