Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains

Abstract

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups $\mathcal{U}$ for $X_n=A_1,$ $B_n,$ $C_n$ and $D_n$. The tool is a modified version of the coordinate Bethe Ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed non-local boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed non-local cases the models are quantum group invariant as well as periodic in a certain sense.

28 pages, plain LaTex, no figures, to appear in Int. J. Mod. Phys. A

References in corpus (4)

• Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions
• A Bethe ansatz solution for the closed $U_q[sl(2)]$ Temperley-Lieb quantum spin chains
• Exact solutions of graded Temperley-Lieb Hamiltonians
• Bethe ansatz solution of the anisotropic correlated electron model associated with the Temperley-Lieb algebra

Cited by in corpus (1)

• Universal Bethe ansatz solution for the Temperley-Lieb spin chain