arXiv:cond-mat/9801129 · Journal of Physics A Mathematical and General

Excitations and theS-matrix for ansu(3)spin chain combining and representations

J Abad, M Ríos

Published Mar 13, 1998• 0 citations

Abstract

The associated Hamiltonian for an su (3) spin chain combining and representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found. The excited states are characterized by means of these quantum numbers. Finally, the exact S -matrix for a state with two holes is found.

DOI: 10.1088/0305-4470/31/10/005

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arXiv:cond-mat/9801129 · Journal of Physics A Mathematical and General

Excitations and theS-matrix for ansu(3)spin chain combining and representations

J Abad, M Ríos

Published Mar 13, 1998• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/31/10/005

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Jan 1, 19982 citations

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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.

Integrable quantum chains combining site states in different representations of

su(3)

The general expression for the local matrix

L(θ)

of a quantum chain with the site space in any representation of

su(3)

is obtained. This is made by generalizing

L(θ)

from the fundamental representation and imposing the fulfilment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of

su(3)

is solved by a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of

su(n)

is presented.