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Journal of Physics A Mathematical and General

Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. II. Thermodynamics of the system

Anatol N. Kirillov, Nicolai Reshetikhin

Published Apr 21, 1987• 56 citations
Publisher

Abstract

For pt.I see ibid., vol.20, p.1565 (1987). The thermodynamics of the integrable generalisation of the XXZ Heisenberg model with arbitrary spin is studied. The low- and high-temperature heat capacities and magnetic susceptibility are computed.
DOI
10.1088/0305-4470/20/6/039

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We consider thermodynamic properties, e.g. specific heat and magnetic susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising symmetry, these chains can be decomposed into a set of finite chain fragments. The problem of finding the thermodynamic quantities is effectively separated into two parts. First we deal with finite objects; secondly we can incorporate the fragments into a statistical ensemble. As functions of the coupling constants, the models exhibit special features in the thermodynamic quantities, e.g. the specific heat displays double peaks at low enough temperatures. These features stem from first-order quantum phase transitions at zero temperature, which have been investigated in the first part of this work.
The finite-size effects in the spectrum of the integrable XXZ Heisenberg chain with arbitrary spin-S are studied analytically on the basis of the string hypothesis for bound states and numerically by solving the associated Bethe ansatz equations. The finite-size corrections to the spectrum and to the low-temperature behaviour of the free energy are found to be similar to the universal predictions for conformally invariant theories, although the model is, in general, not Lorentz invariant, since it can have an arbitrary number of branches for low-energy excitations with different Fermi velocities depending on the value of S and the anisotropy parameter gamma .