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

Zengo Tsuboi
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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.

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Zengo Tsuboi. 2002-12-12. Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model. https://doi.org/10.1088/0305-4470%2F36%2F5%2F321

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