Non-Hermitian spin chains with inhomogeneous coupling

Details Non-Hermitian spin chains with inhomogeneous coupling Non-Hermitian spin chains with inhomogeneous coupling

2009-11-23

arxiv.org/abs/0911.4476v3

Alg.Anal.22N3:80-106,2010; St.Petersburg Math.J.22:393-410,2011

Physics

Mathematical Physics

19 pages, LaTeX; v.3 - a proof of eq.(52) added

Scientific paper

An open U_q(sl_2)-invariant spin chain of spin S and length N with inhomogeneous coupling is investigated as an example of a non-Hermitian (quasi-Hermitian) model. For several particular cases of such a chain, the ranges of the deformation parameter gamma are determined for which the spectrum of the model is real. For a certain range of gamma, a universal metric operator is constructed and thus the quasi-Hermiticity of the model is established. The constructed metric operator is non-dynamical, its structure is determined only by the symmetry of the model. The results apply, in particular, to all known homogeneous U_q(sl_2)-invariant integrable spin chains with nearest-neighbour interaction. In addition, the most general form of a metric operator for a quasi-Hermitian operator in finite dimensional space is discussed.

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