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Non-Hermitian spin chains with inhomogeneous coupling | | Andrei G. Bytsko
; | | Date: |
23 Nov 2009 | | 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. | | Source: | arXiv, 0911.4476 | | Services: | Forum | Review | PDF | Favorites | |
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