T-W relation and free energy of the Heisenberg chain at a finite temperature

TL;DR

This paper derives a new nonlinear integral equation for the thermodynamics of the Heisenberg spin chain using the t-W relation, enabling calculation of free energy and generalization to other models.

Contribution

It introduces a novel NLIE based on the t-W relation for the Heisenberg chain and demonstrates its applicability to other integrable models like the SU(3) spin chain.

Findings

Exact free energy matches previous results.

Method generalizes to other lattice quantum integrable models.

Provides a new approach for thermodynamic calculations.

Abstract

A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t-W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corresponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.