PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain

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dc.creatorKorff, Christian
dc.creatorWeston, Robert A.
dc.date2007-03-29
dc.date2007-07-12
dc.date.accessioned2026-07-07T11:03:18Z
dc.date.available2026-07-07T11:03:18Z
dc.descriptionWe 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 relys 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.
dc.description32 pages with figures, v2: some minor changes and added references, version published in JPA
dc.identifierhttps://arxiv.org/abs/math-ph/0703085
dc.identifierhttp://arxiv.org/abs/math-ph/0703085
dc.identifierJ.Phys.A40:8845-8872,2007
dc.identifierdoi:10.1088/1751-8113/40/30/016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/188549
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titlePT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
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