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

2005/05/31 by Jan de Gier, Alexander Nichols, Pavel Pyatov +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2005.09.005

published as Nucl.Phys.B729:387-418,2005 · 29 pages

arxiv created 2005/08/12 · openalex publication_date 2005/09/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that from the spectra of the Uq (sl(2)) symmetric XXZ spin-1/2 finite quantum chain at Delta=-1/2 (q=epi 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=epi 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.

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