Regensburg 2010 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 30: CE: Low-dimensional Systems - Models 1

TT 30.3: Talk

Thursday, March 25, 2010, 10:00–10:15, H20

Quantum spin chains of Temperley-Lieb type with periodic boundary conditions: spectra, multiplicities and finite temperature — •Britta Aufgebauer and Andreas Klümper — Universität Wuppertal

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the XXZ chain as a reference system. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sectorwise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Further the representation theoretical results allow for the study of the thermodynamics by establishing a ‘ TL-equivalence at finite temperature and finite field’.