Non-Hermitian spin chains with inhomogeneous coupling
Abstract
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.
Cite
@article{arxiv.0911.4476,
title = {Non-Hermitian spin chains with inhomogeneous coupling},
author = {Andrei G. Bytsko},
journal= {arXiv preprint arXiv:0911.4476},
year = {2011}
}
Comments
19 pages, LaTeX; v.3 - a proof of eq.(52) added