Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2

Abstract

We show that from the spectra of the U_q (sl(2)) symmetric XXZ spin-1/2 finite quantum chain at Delta=-1/2 (q=e^{pi i/3}) one can obtain the spectra of certain XXZ quantum chains with diagonal and non-diagonal boundary conditions. Similar observations are made for Delta=0 (q=e^{pi i/2}). In the finite-size scaling limit the relations among the various spectra are the result of identities satisfied by known character functions. For the finite chains the origin of the remarkable spectral identities can be found in the representation theory of one and two boundaries Temperley-Lieb algebras at exceptional points. Inspired by these observations we have discovered other spectral identities between chains with different boundary conditions.

29 pages

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Cited by in corpus (58)

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• The open XXZ and associated models at q root of unity
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• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
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• Exact finite size groundstate of the O(n=1) loop model with open boundaries
• Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries
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• On the supersymmetric vacua of the Veneziano-Wosiek model
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