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Exact solution of the SU q (n) invariant quantum spin chains

Paris Vi

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the An−1 vertex model with fixed open boundary conditions and the corresponding SUq(n) invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.

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The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the An−1 vertex model with fixed open boundary conditions and the corresponding SUq(n) invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.
Exact solution of the SUq(n)SU_{q}(n)SUq​(n) invariant quantum spin chains
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the An−1A_{n-1}An−1​ vertex model with fixed open boundary conditions and the corresponding SUq(n)SU_{q}(n)SUq​(n) invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.
We present in a unified and detailed way the nested Bethe ansatz for open spin chains based on(super)algebras, with arbitrary representations (i.e., 'spins') on each site of the chain and diagonal boundary matrices (K + (u), K -(u)).The nested Bethe ansatz applies for a general K -(u), but a particular form of the K + (u) matrix.The construction extends and unifies the results already obtained for open spin chains based on the fundamental representation and for some particular superspin chains.We give the eigenvalues, Bethe equations and the explicit form of the Bethe vectors for the corresponding models.The Bethe vectors are also expressed using a trace formula.