Thermodynamics of the quantum spin-S XXZ chain

TL;DR

This paper derives high-temperature expansions for the thermodynamics of the quantum spin-$S$ XXZ chain, analyzing classical limits and comparing results with numerical data for various spin values.

Contribution

It provides a $eta$-expansion of the Helmholtz free energy for arbitrary spin $S$, including effects of anisotropy and magnetic field, and explores the classical limit as $S o \infty$.

Findings

High-temperature expansion matches Joyce's exact solution at $h=0$, $D=0$.

Thermodynamic functions approach classical behavior for large $S$.

Interpolation of high- and low-temperature data agrees with numerical results.

Abstract

The thermodynamics of the spin-$S$ anisotropic quantum $XXZ$ chain with arbitrary value of $S$ and unitary norm, in the high-temperature regime, is reported. The single-ion anisotropy term and the interaction with an external magnetic field in the $z$-direction are taken into account. We obtain, for arbitrary value of $S$, the $\beta$-expansion of the Helmholtz free energy of the model up to order $\beta^6$ and show that it actually depends on $\frac{1}{S(S+1)}$. Its classical limit is obtained by simply taking $S\to \infty$. At $h=0$ and D=0, our high temperature expansion of the classical model coincides with Joyce's exact solution\cite{joyce_prl}. We study, in the high temperature region, some thermodynamic quantities such as the specific heat and the magnetic susceptibility as functions of spin and verify for which values of $S$ those thermodynamic functions behave classically. Their finite temperature behavior is inferred from interpolation of their high- and low-temperature behavior, and shown to be in good agreement with numerical results. The finite temperature behavior is shown for higher values of spin.