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

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

2007-03-29

arxiv.org/abs/math-ph/0703085v2

J.Phys.A40:8845-8872,2007

Physics

Mathematical Physics

32 pages with figures, v2: some minor changes and added references, version published in JPA

Scientific paper

10.1088/1751-8113/40/30/016

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 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.

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