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Excitations and S-matrix for su(3) spin chain combining {3} and {3 ∗ } representations

J. Abad, M. Ríos

Published Jan 1, 1998• 2 citations
OpenAlex

Abstract

The associated Hamiltonian for a su(3) spin chain combining {3} and {3 ∗ } 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. PACS

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The associated Hamiltonian for a su(3) spin chain combining {3} and {3 ∗ } 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. PACS
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Integrable quantum chains combining site states in different representations of su(3)su(3)su(3)
The general expression for the local matrix L(θ)L(θ)L(θ) of a quantum chain with the site space in any representation of su(3)su(3)su(3) is obtained. This is made by generalizing L(θ)L(θ)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)su(3)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)su(n)su(n) is presented.
We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish — Reshetikhin by considering also complex “string” solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1, …, N − 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N − 1 ]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N−l) × U(1), as well as a new “duality” symmetry which maps l→N−l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N − 1 ] the corresponding boundary S-matrices.