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We determine the spectra of a class of quantum spin chains of Temperley-Liebtype by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZchain as a reference system. We consider open boundary conditions and inparticular periodic boundary conditions. For both types of boundaries theidentification with XXZ spectra is performed within isomorphic representationsof the underlying Temperley-Lieb algebra. For open boundaries the spectra ofthese models differ from the spectrum of the associated XXZ chain only in themultiplicities of the eigenvalues. The periodic case is rather different. Herewe show how the spectrum is obtained sector-wise from the spectra of globallytwisted XXZ chains. As a spin-off, we obtain a compact formula for thedegeneracy of the momentum operator eigenvalues. Our representation theoreticalresults allow for the study of the thermodynamics by establishing aTL-equivalence at finite temperature and finite field.

Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature