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

Korff, C. and Weston, R. (2007) PT symmetry on the lattice: the quantum group invariant XXZ spin chain. Journal of Physics A: Mathematical and Theoretical, 40(30), pp. 8845-8872. (doi:10.1088/1751-8113/40/30/016)

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Publisher's URL: http://dx.doi.org/10.1088/1751-8113/40/30/016

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Korff, Dr Christian
Authors: Korff, C., and Weston, R.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Physics A: Mathematical and Theoretical
ISSN:1751-8113
ISSN (Online):1751-8121

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