Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2000-03-30
Nonlinear Sciences
Exactly Solvable and Integrable Systems
28 pages, plain LaTex, no figures, to appear in Int. J. Mod. Phys. A
Scientific paper
10.1142/S0217751X00001243
We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ 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.
Ghiotto R. C. T.
Malvezzi Andre Luiz
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