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arXiv:hep-th/9303043 · Physical review. B, Condensed matter

Thermodynamics of integrable chains with alternating spins

Hector J. de Vega, Luca Mezincescu, Rafael I. Nepomechie

Published May 1, 1994• 66 citations
arXivHTMLPDF

Abstract

We consider a two-parameter (c\ifmmode\bar\else\textasciimacron\fi{},c\ifmmode \tilde{}\else \~{}\fi{}) family of quantum integrable isotropic Hamiltonians for a chain of alternating spins of spin s=1/2 and s=1. We determine the thermodynamics for low-temperature T and small external magnetic field H, with T\ensuremath{\ll}H. In the antiferromagnetic (c\ifmmode\bar\else\textasciimacron\fi{}>0,c\ifmmode \tilde{}\else \~{}\fi{}>0) case, the model has two gapless excitations. In particular, for c\ifmmode\bar\else\textasciimacron\fi{}=c\ifmmode \tilde{}\else \~{}\fi{}, the model is conformally invariant and has central charge ${\mathit{c}}_{\mathrm{vir}}$=2. When one of these parameters is zero, the Bethe ansatz equations admit an infinite number of solutions with lowest energy.

DOI
10.1103/physrevb.49.13223

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We consider a two-parameter (c\ifmmode\bar\else\textasciimacron\fi{},c\ifmmode \tilde{}\else ~{}\fi{}) family of quantum integrable isotropic Hamiltonians for a chain of alternating spins of spin s=1/2 and s=1. We determine the thermodynamics for low-temperature T and small external magnetic field H, with T\ensuremath{\ll}H. In the antiferromagnetic (c\ifmmode\bar\else\textasciimacron\fi{}>0,c\ifmmode \tilde{}\else ~{}\fi{}>0) case, the model has two gapless excitations. In particular, for c\ifmmode\bar\else\textasciimacron\fi{}=c\ifmmode \tilde{}\else ~{}\fi{}, the model is conformally invariant and has central charge cvir{\mathit{c}}_{\mathrm{vir}}cvir​=2. When one of these parameters is zero, the Bethe ansatz equations admit an infinite number of solutions with lowest energy.
In this paper we continue the investigation of an anisotropic integrable spin chain, consisting of spins s = 1 and , started in our paper (Meiß ner St and Dörfel B-D 1996 J. Phys. A: Math. Gen. 29 1949) . The thermodynamic Bethe ansatz is analysed especially for the case, when the signs of the two couplings and differ. For the conformally invariant model we have calculated heat capacity and magnetic susceptibility at low temperature. In the isotropic limit our analysis is carried out further and susceptibilities are calculated near phase transition lines (at T = 0).
Abstract This chapter presents the extension of the Bethe ansatz to finite temperature, the thermodynamic Bethe ansatz, for the antiferromagnetic isotropic Heisenberg quantum spin chain, the XXX quantum spin chain. It discusses how the added complications of this model arise from the more complicated structure of excitations of the quantum spin chain, the complex string excitations, which have to be included in the Bethe ansatz thermodynamics. It derives the integral equations of the thermodynamic Bethe ansatz for the XXX quantum spin chain and mentions explicit formulas for the free energy of the quantum spin chain and some interesting physical quantities, especially making contact with predictions of conformal symmetry.
The equations of the thermodynamic Bethe ansatz for two-chain and multichain quantum spin 1/2 systems are constructed. It is shown that the system is in the antichiral state for any temperature range and for any value of the external magnetic field (except for the ferromagnetic ground-state case). The elementary spin excitations carry nonzero chirality and are gapless. Those excitations are confined into pairs (singlets and triplets), with opposite sign of chiralities, so the state of the system remains antichiral at any temperature. The reason for such chiral behavior is the existence of the topological term of the Wess-Zumino nature in the Hamiltonian. We conjecture that the quantum spin (1/2) multichain system with the Hamiltonian without the topological terms has excitations with gaps.
We study an integrable spin chain with an alternating array of spins S=1/2, 1 in external magnetic fields using the Bethe ansatz exact solution. The calculated magnetization possesses a cusp structure at a critical magnetic field H=H_{C}, at which the specific heat shows a divergence property. We also calculate finite-size corrections to the energy spectrum, and obtain the critical exponents of correlation functions with the use of conformal field theory (CFT). Low-energy properties of the model are described by two c=1 U(1) CFTs in HH_{C}.
The sector of zero ZN charge is studied for the ferromagnetic (FM) and antiferromagnetic (AFM) version of the (ZN×Z2)-invariant Fateev-Zamolodchikov quantum spin chain. We conjecture that the relevant Bethe ansatz equations should admit, besides the usual stringlike solutions, exceptional multiplets, and a number of nonphysical solutions. Once the physical ones are identified, we show how completeness and the gapless excitation spectrum can be obtained. The central charge is computed from the specific heat and found to be [Formula: see text] (FM) and c=1 (AFM).