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

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.

24 pages, 4 figures, to appear in J. Phys. A: Math. Gen

References in corpus (7)

• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Analytic Bethe ansatz and functional equations for Lie superalgebra sl(r+1|s+1)
• Analytic Bethe ansatz related to a one parameter family of finite dimensional representations of the Lie superalgebra sl(r+1|s+1)
• Analytic Bethe ansatz and functional relations related to tensor-like representations of type II Lie superalgebras B(r|s) and D(r|s)
• Analytic Bethe ansatz related to the Lie superalgebra C(s)
• Direct Calculation of Thermodynamic Quantities for Heisenberg Model
• Integral equations for thermodynamics of the osp(1|2s) integrable spin chain

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• Exact results for the thermal and magnetic properties of strong coupling ladder compounds
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• Nonlinear Integral Equations and high temperature expansion for the $U_q(\widehat{sl}(r+1|s+1))$ Perk-Schultz Model
• Fusion hierarchies for N = 4 superYang-Mills theory
• Thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies
• Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model
• From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model
• Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds
• Nonlinear Integral Equations for Thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz Model
• Exact solution and magnetic properties of an anisotropic spin ladder
• T-W relation and free energy of the Heisenberg chain at a finite temperature