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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 80–106 (Mi aa1187)

Research Papers

Non-Hermitian spin chains with inhomogeneous coupling

A. G. Bytsko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

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-Hermitian nature of the model is established. This universal metric operator is nondynamical, 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-neighbor interaction. In addition, the most general form of a metric operator for a quasi-Hermitian operator in finite-dimensional spaces is discussed.

Keywords: quasi-Hermitian Hamiltonians, quantum algebras, spin chains.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:3, 393–410

Bibliographic databases:

Citation: A. G. Bytsko, “Non-Hermitian spin chains with inhomogeneous coupling”, Algebra i Analiz, 22:3 (2010), 80–106; St. Petersburg Math. J., 22:3 (2011), 393–410

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Fring A., “Pt-Symmetric Deformations of Integrable Models”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 371:1989, SI (2013), 20120046
2. Bytsko A., “Tensor Space Representations of Temperley-Lieb Algebra Via Orthogonal Projections of Rank R >= 1”, J. Math. Phys., 56:8 (2015), 083502
3. Li C., Song Z., “Generation of Bell, W, and Greenberger-Horne-Zeilinger States Via Exceptional Points in Non-Hermitian Quantum Spin Systems”, Phys. Rev. A, 91:6 (2015), 062104
4. Viennot D., Aubourg L., “Quantum Chimera States”, Phys. Lett. A, 380:5-6 (2016), 678–683
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