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.
|Number of pages||28|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 27 Jul 2007|