Second cluster integral from the spectrum of an infinite XXZ spin chain

TL;DR

This paper derives the first two terms of the low-temperature cluster expansion for the free energy of an infinite XXZ spin chain using a propagator approach based on one- and two-magnon spectra, reproducing known results at the XXX point.

Contribution

It introduces a propagator-based method to compute low-temperature cluster expansion terms using only one- and two-magnon spectra for the XXZ chain.

Findings

Derived the first and second cluster expansion terms for the XXZ chain

Reproduced Katsura's formula at the XXX point

Validated the propagator approach with known spectral data

Abstract

First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized $XXZ$ spin chain is obtained within the propagator approach suggested by E. W. Montroll and J. C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the $XXX$-point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.