Thermodynamics of an Ising-like XXZ chain in a longitudinal magnetic field in the framework of the Quantum Transfer Matrix approach

TL;DR

This paper derives a perturbative expression for the free energy of an anisotropic Heisenberg-Ising chain using the Quantum Transfer Matrix method, aligning with high- and low-temperature expansions.

Contribution

It introduces a perturbative approach for the free energy of the Heisenberg-Ising chain with strong anisotropy within the Quantum Transfer Matrix framework.

Findings

Results agree with high-temperature expansion

Results agree with low-temperature cluster expansion in specific regimes

Provides a new analytical tool for thermodynamics of anisotropic spin chains

Abstract

Taking the Ising chain as a reference model we have derived a perturbative expression for the free energy density of the Heisenberg-Ising chain with strong easy-axis anisotropy. All calculations are performed on the ground of the Quantum Transfer Matrix approach. The obtained result agrees with the direct high-temperature expansion. It also agrees with the low-temperature cluster expansion in the special subregime when quantum fluctuations are weak against thermodynamical ones.