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arXiv:hep-th/9609134 · Journal of Physics A Mathematical and General

Finite-size corrections of an integrable chain with alternating spins

B-D Dörfel, St Meissner

Published Mar 21, 1997• 9 citations
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Abstract

In this paper we calculate the finite-size corrections of an anisotropic integrable spin chain, consisting of spins s = 1 and . The calculations are done in two regions of the phase diagram with respect to the two couplings and . In the case of conformal invariance we obtain the final answer for the ground state and its lowest excitations, which generalizes earlier results.

DOI
10.1088/0305-4470/30/6/010

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In this paper we calculate the finite-size corrections of an anisotropic integrable spin chain, consisting of spins s = 1 and . The calculations are done in two regions of the phase diagram with respect to the two couplings and . In the case of conformal invariance we obtain the final answer for the ground state and its lowest excitations, which generalizes earlier results.
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).
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.
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.
Leading and next-to-leading-order finite-size corrections to the ground and first excited states are calculated for the spin-1/2 anisotropic Heisenberg model in the critical region. The analytic results are compared to numerical data obtained for chains up to a length of N=1024. It is found that, near the isotropic point, the asymptotic region where the results obtained for N to infinity are applicable sets in at very large N values, and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms, even at large (N>100) chain lengths.
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.