Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model

TL;DR

This paper derives and compares thermodynamic Bethe ansatz equations and new nonlinear integral equations for the sl(r+1) Uimin-Sutherland model, simplifying calculations and connecting to known models.

Contribution

It introduces a new family of nonlinear integral equations for the model, including a finite subset that simplifies analysis and relates to existing equations.

Findings

Derived TBA equations from T-system match string hypothesis results.

Established a new finite set of NLIEs reducing complexity.

Calculated high temperature free energy expansion using the new NLIEs.

Abstract

We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number of unknown functions. For r=1, this subset of NLIE reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIE is clarified. Based on our new NLIE, we also calculate the high temperature expansion of the free energy.