Exact solution of A-D Temperley-Lieb Models
نویسنده
چکیده
We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups Uq(Xn) for Xn = A1, Bn, Cn and Dn. We employ a generalization of the coordinate Bethe-Ansatz developed previously for the deformed biquadratic spin one chain. As expected, all these models have equivalent spectra, i.e. they differ only in the degeneracy of their eigenvalues. This is true for finite length and open boundary conditions. For periodic boundary conditions the spectra of the lower dimensional representations are containded entirely in the higher dimensional ones. The Bethe states are highest weight states of the quantum group, except for some states with energy zero. ∗ On leave of abscence from Instituto de F́ısica de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos 13560-970 , Brasil. † Supported in part by CNPq-BRASIL.
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