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arXiv:hep-th/9212125 · Nuclear Physics B

Low-temperature thermodynamics of A2(2) and su(3)-invariant integrable spin chains

Luca Mezincescu, Rafael I. Nepomechie, Paul K. Townsend, Alexei M. Tsvelik

Published Oct 1, 1993• 32 citations
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Abstract

We formulate the thermodynamic Bethe ansatz (TBA) equations for the closed (periodic boundary conditions) A2(2) quantum spin chain in an external magnetic field, in the (noncritical) regime where the anisotropy parameter η is real. In the limit η → 0, we recover the TBA equations of the antiferromagnetic integrable su(3)-invariant chain in the fundamental representation. We solve these equations for low temperature and small field, and calculate the specific heat and magnetic susceptibility.

DOI
10.1016/0550-3213(93)90006-b

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We formulate the thermodynamic Bethe ansatz (TBA) equations for the closed (periodic boundary conditions) A2(2) quantum spin chain in an external magnetic field, in the (noncritical) regime where the anisotropy parameter η is real. In the limit η → 0, we recover the TBA equations of the antiferromagnetic integrable su(3)-invariant chain in the fundamental representation. We solve these equations for low temperature and small field, and calculate the specific heat and magnetic susceptibility.
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.
We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz (BA) method. In particular, we determine in this way the spectrum of the transfer matrices of the Uq[su(2)]-invariant spin chains associated with A1(1) and A2(2) in the fundamental representation. The quantum-algebra invariance of these models plays an essential role in obtaining these results. The BA equations for these open chains are “doubled” with respect to the BA equations for the corresponding closed chains.
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).