From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

TL;DR

This paper derives a simplified nonlinear integral equation for the thermodynamics of the higher spin Heisenberg model, utilizing advanced algebraic formulas, and computes key thermodynamic quantities at high temperatures.

Contribution

It introduces a novel NLIE with a single unknown function for arbitrary spin, based on the quantum Jacobi-Trudi and Giambelli formula, advancing the analytical understanding of the model's thermodynamics.

Findings

Derived a single-function NLIE for free energy

Calculated high-temperature specific heat expansion

Computed magnetic susceptibility at high temperatures

Abstract

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.