Equivalence between a bosonic theory and a massive non-local Thirring model at Finite Temperature

TL;DR

This paper demonstrates the equivalence between a massive non-local Thirring model and a non-local sine-Gordon theory at finite temperature using path-integral bosonization, extending Coleman's zero-temperature result to finite temperature.

Contribution

It generalizes Coleman's equivalence to finite temperature for models with non-local interactions, providing explicit partition function comparisons.

Findings

Fermionic and bosonic expansions match term by term under certain conditions.

The equivalence holds for specific relationships between the potentials.

The results are relevant for strongly correlated one-dimensional systems.

Abstract

Using the path-integral bosonization procedure at Finite Temperature we study the equivalence between a massive Thirring model with non-local interaction between currents (NLMT) and a non-local extension of the sine-Gordon theory (NLSG). To this end we make a perturbative expansion in the mass parameter of the NLMT model and in the cosine term of the NLSG theory in order to obtain explicit expressions for the corresponding partition functions. We conclude that for certain relationship between NLMT and NLSG potentials both the fermionic and bosonic expansions are equal term by term. This result constitutes a generalization of Coleman's equivalence at T=0, when considering a Thirring model with bilocal potentials in the interaction term at Finite Temperature. The study of this model is relevant in connection with the physics of strongly correlated systems in one spatial dimension. Indeed, in the language of many-body non-relativistic systems, the relativistic mass term can be shown to represent the introduction of backward-scattering effects.