TBA and tree expansion

TL;DR

This paper introduces a statistical derivation of the Thermodynamic Bethe Ansatz using tree expansion of the Gaudin determinant, successfully reproducing key physical quantities in integrable models.

Contribution

It presents a novel, tree expansion-based method for deriving the Thermodynamic Bethe Ansatz, applicable to theories with diagonal scattering.

Findings

Reproduces free energy density expressions

Derives finite size corrections for excited states

Obtains LeClair-Mussardo series for local operators

Abstract

We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound states. We reproduce the expression for the free energy density and the finite size corrections to the energy of an excited state as well as the LeClair-Mussardo series for the one-point function for local operators.