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Ground state and low excitations of an integrable chain with alternating spins

Meissner, S, B -D Dorfel

Published Jan 1, 1995• 6 citations
OpenAlex

Abstract

An anisotropic integrable spin chain, consisting of spins $s=1$ and $s=\frac{1}{2}$, is investigated \cite{devega}. It is characterized by two real parameters $\bar{c}$ and $\tilde{c}$, the coupling constants of the spin interactions. For the case $\bar{c}<0$ and $\tilde{c}<0$ 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.

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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.
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.
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 verifies the conjecture for the wave function, the Bethe ansatz wave function, of the anisotropic Heisenberg quantum spin chain by examining first the cases for one, two, and three spin deviations. The equations determining the quasi- momenta are the Bethe ansatz equations, now obtained from the coordinate Bethe ansatz. The Bethe ansatz equations derive from the eigenvalue equation in combination with boundary conditions, here periodic boundary conditions. These quasi-momenta also determine the energy eigenvalue. However, solving the Bethe ansatz equations to obtain a particular state requires more considerations. New variables, called rapidities, are useful. The consideration of the thermodynamic limit then allows to extract information about the ground state and low-lying excitations of the anisotropic quantum spin chain from the Bethe ansatz equations. Furthermore, complex solutions of the Bethe ansatz equations, called strings, are considered.
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.