Kinks versus fermions or the 2D sine-Gordon versus massive Thirring models, at nonzero temperature and chemical potential

TL;DR

This paper investigates the equivalence of the massive Thirring and sine-Gordon models at finite temperature and chemical potential, revealing how thermal effects and topological terms influence their relationship and excitations.

Contribution

It proves the equivalence of the models at finite temperature and zero chemical potential, and extends the analysis to nonzero chemical potential showing additional topological terms.

Findings

Partition functions of the models are equal at finite T and zero chemical potential.

Thermal averages of zero-charge operators are identified across models.

At nonzero chemical potential, the bosonised theory includes an extra topological term.

Abstract

We study bosonisation in the massive Thirring and sine-Gordon models at finite temperature and nonzero fermion chemical potential. Both canonical operator and path integral approaches are used to prove the equality of the partition functions of the two models at finite $T$ and zero chemical potential, as it has been recently shown. This enables the relationship between thermal normal ordering and path-integral renormalisation to be specified. Furthermore, we prove that thermal averages of zero-charge operators can also be identified. At nonzero chemical potential and temperature we show, in perturbation theory around the massless case, that the bosonised theory is the sine-Gordon model plus an additional topological term, accounting for the existence of zero charge excitations (the fermions or the kinks) in the thermal bath. This result is the 2D version of the low-energy lagrangian at finite baryon density.