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arXiv:hep-th/9708107 · Journal of Physics A Mathematical and General

Complete phase diagram for the integrable chain with alternating spins in the sectors with competing interactions

B-D Dörfel, St Meißner

Published Jan 9, 1998• 3 citations
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Abstract

We investigate the anisotropic integrable spin chain consisting of spins and s = 1 by means of thermodynamic Bethe ansatz for the anisotropy , where the analysis of the Takahashi conditions leads to a more complicated string picture. We give the phase diagram with respect to the two real coupling constants and , which contain a new region where the ground state is formed by strings with infinite Fermi zones. In this region the velocities of sound for the two physical excitations have been calculated from the dressed energies. This leads to an additional line of conformal invariance not known before.

DOI
10.1088/0305-4470/31/1/011

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We investigate the anisotropic integrable spin chain consisting of spins and s = 1 by means of thermodynamic Bethe ansatz for the anisotropy , where the analysis of the Takahashi conditions leads to a more complicated string picture. We give the phase diagram with respect to the two real coupling constants and , which contain a new region where the ground state is formed by strings with infinite Fermi zones. In this region the velocities of sound for the two physical excitations have been calculated from the dressed energies. This leads to an additional line of conformal invariance not known before.
We investigate the anisotropic integrable chain consisting of spins and s = 1. Depending on the anisotropy and the ratio of the coupling constants it has different (antiferromagnetic) ground states, manifesting themselves in a different string content in the Bethe ansatz framework. In this paper we continue the study of those regions with different string content, below called sectors. First we compare the dispersion relations for the sectors with infinite Fermi zones. Further we calculate the speeds of sound for regions close to sector borders, where the Fermi radii either vanish or diverge, and compare the results.
An anisotropic integrable spin chain, consisting of spins s=1s=1s=1 and s=12s=\frac{1}{2}s=21​, is investigated \cite{devega}. It is characterized by two real parameters cˉ\bar{c}cˉ and c~\tilde{c}c~, the coupling constants of the spin interactions. For the case cˉ<0\bar{c}<0cˉ<0 and c~<0\tilde{c}<0c~<0 the ground state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore the low excitations are calculated. It turns out, that apart from free magnon states being the holes in the ground state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to \cite{babelon}. The dispersion law of these excitations is calculated numerically.
An anisotropic integrable spin chain, consisting of spins s = 1 and , is investigated [1]. It is characterized by two real parameters and , the coupling constants of the spin interactions. For the case and the ground-state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore, the low excitations are calculated. It turns out that apart from free magnon states being the holes in the ground-state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to [13]. The dispersion law of these excitations is calculated numerically.
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).
A general procedure to generate new integrable Hamiltonians combining to any kind of spins distributed arbitrarily on the line is given. As a concrete application, anisotropic chains formed by spin-1/2 and spin-1 operators at alternating sites are presented and solved exactly by the Bethe ansatz (BA). The authors compute the ground-state and excitation energies and momentum. The higher-order BA equations are derived. Depending on the choice, these new Hamiltonians exhibit, or not, conformal invariance in their low energy spectrum.