Simple Approach to Thermal Bethe Ansatz

TL;DR

This paper introduces a new, simplified method using a single non-linear integral equation to calculate thermodynamic functions for Bethe Ansatz solvable models, including the XXZ Heisenberg chain and Sine-Gordon theory.

Contribution

It derives a unified non-linear integral equation for thermodynamics and finite-size energies, simplifying previous multi-equation approaches for crossing-invariant models.

Findings

Exact free energy calculation for XXZ chain at arbitrary anisotropy.

Systematic high-temperature expansion from the integral equations.

Correct low-temperature behavior including central charge and analytic structure.

Abstract

We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear integral equation from which the free energy can be exactly calculated.These equations are shown to be equivalent to an infinite set of algebraic equations of Bethe type which provide alternatively the thermodinamics. The high-temperature expansion follows in a sistematic and relatively simple way from our non-linear integral equations. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around T=0. Furthermore, we derive a single non-linear integral equation describing the finite-size ground-state energy of the Sine-Gordon quantum field theory.