Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains

TL;DR

This paper investigates the thermodynamic properties of the anisotropic spin-1/2 Heisenberg chain and related models using quantum transfer matrix methods, deriving integral equations and comparing results with conformal field theory predictions.

Contribution

It introduces a comprehensive quantum transfer matrix approach to analyze finite-temperature behavior of anisotropic quantum chains, including new integral equations and numerical solutions.

Findings

Analytic low-temperature asymptotics for the critical XXZ chain in magnetic field.

Numerical solutions for non-critical XXZ and spin-1 biquadratic chains at arbitrary temperatures.

Comparison of results with conformal field theory predictions.

Abstract

The free energy and correlation lengths of the spin-1/2 $XYZ$ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the critical $XXZ$ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-critical $XXZ$ chain and the related spin-1 biquadratic chain at arbitrary temperature.