A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model

TL;DR

This paper presents a direct method to compute the free energy of the XXX Heisenberg model using the Bethe ansatz equation, providing a more straightforward approach than previous methods.

Contribution

It introduces a novel, direct calculation technique for the free energy based solely on the Bethe ansatz equation, simplifying the thermodynamic analysis.

Findings

The trace of the Boltzmann weight explains the string hypothesis.

The free energy can be derived directly from the Bethe ansatz equation.

The method is more straightforward than previous approaches.

Abstract

Thermodynamics of the XXX Heisenberg model is studied. The trace of the Boltzmann weight with respect to the Hilbert space is taken in the thermodynamic limit with the number of up-spins being fixed. The expression of the trace gives an explanation why the correct thermodynamic quantities are derived from the string hypothesis. Combining this with the previous result, we conclude that the free energy can be calculated only by assuming the Bethe ansatz equation. The method is more direct than other known methods which were used to derive the free energy.