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

TL;DR

This paper analyzes an integrable spin chain with alternating spins 1 and 1/2, deriving its ground state and low-energy excitations using thermodynamic Bethe ansatz, revealing free magnons and bound states.

Contribution

It introduces a detailed analysis of an anisotropic integrable spin chain with mixed spins, including ground state configuration and excitation spectrum, using Bethe ansatz methods.

Findings

Ground state configuration obtained via thermodynamic Bethe ansatz.

Existence of free magnon states as holes in the rapidity distribution.

Presence of bound states described by string solutions of Bethe ansatz equations.

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.