Chiral Symmetry restoration in the massive Thirring model at finite T and $\mu$: Dimensional reduction and the Coulomb gas

TL;DR

This paper demonstrates the equivalence of the (1+1)-dimensional massive Thirring model at finite temperature to a Coulomb gas, revealing phase transitions and chiral symmetry restoration mechanisms relevant to low-energy QCD.

Contribution

It establishes a novel equivalence between the massive Thirring model and a Coulomb gas, providing insights into phase structure and symmetry restoration at finite temperature and chemical potential.

Findings

At high T, the system behaves as a free gas of charge pairs.

Chiral symmetry is restored as T approaches infinity.

Finite chemical potential leads to chiral restoration via vanishing fermion mass.

Abstract

We show that in certain limits the (1+1)-dimensional massive Thirring model at finite temperature $T$ is equivalent to a one-dimensional Coulomb gas of charged particles at the same $T$. This equivalence is then used to explore the phase structure of the massive Thirring model. For strong coupling and $T>>m$ (the fermion mass) the system is shown to behave as a free gas of "molecules" (charge pairs in the Coulomb gas terminology) made of pairs of chiral condensates. This binding of chiral condensates is responsible for the restoration of chiral symmetry as $T\to\infty$. In addition, when a fermion chemical potential $\mu\neq 0$ is included, the analogy with a Coulomb gas still holds with $\mu$ playing the role of a purely imaginary external electric field. For small $T$ and $\mu$ we find a typical massive Fermi gas behaviour for the fermion density, whereas for large $\mu$ it shows chiral restoration by means of a vanishing effective fermion mass. Some similarities with the chiral properties of low-energy QCD at finite $T$ and baryon chemical potential are discussed.