PT symmetry on the lattice: The quantum group invariant XXZ spin chain

Christian Korff, Robert Weston

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

We investigate the PT-symmetry of the quantum group invariant XXZ chain. We show that the PT-operator commutes with the quantum group action and also discuss the transformation properties of the Bethe wavefunction. We exploit the fact that the Hamiltonian is an element of the Temperley-Lieb algebra in order to give an explicit and exact construction of an operator that ensures quasi-Hermiticity of the model. This construction relies on earlier ideas related to quantum group reduction. We then employ this result in connection with the quantum analogue of Schur-Weyl duality to introduce a dual pair of C-operators, both of which have closed algebraic expressions. These are novel, exact results connecting the research areas of integrable lattice systems and non-Hermitian Hamiltonians. © 2007 IOP Publishing Ltd.

Original languageEnglish
Article number016
Pages (from-to)8845-8872
Number of pages28
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number30
DOIs
Publication statusPublished - 27 Jul 2007

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