Nonlinear Integral Equations and high temperature expansion for the $U_{q}(\hat{sl}(r+1|s+1))$ Perk-Schultz Model

TL;DR

This paper introduces a simplified system of nonlinear integral equations for the $U_q( ext{sl}(r+1|s+1))$ Perk-Schultz model, enabling efficient high-temperature free energy calculations and expansions.

Contribution

It presents a novel set of NLIE with fewer unknowns, utilizing supersymmetric identities, to analyze the Perk-Schultz model's thermodynamics.

Findings

Derived NLIE with r+s+1 unknown functions

Calculated high temperature expansion coefficients up to order 5

Extended specific heat expansion up to order 40

Abstract

We propose a system of nonlinear integral equations (NLIE) which gives the free energy of the $U_{q}(widehat{sl}(r+1|s+1))$ Perk-Schultz model. In contrast with traditional thermodynamic Bethe ansatz equations, our NLIE contain only r+s+1 unknown functions. In deriving the NLIE, the quantum (supersymmetric) Jacobi-Trudi and Giambelli formula and a duality for an auxiliary function play important roles. By using our NLIE, we also calculate the high temperature expansion of the free energy. General formulae of the coefficients with respect to arbitrarily rank r+s+1, chemical potentials $\{\mu_{a}\}$ and q have been written down in terms of characters up to the order of 5. In particular for specific values of the parameters, we have calculated the high temperature expansion of the specific heat up to the order of 40.