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

This article is cited in 4 scientific papers (total in 4 papers)

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:

Received: 18.12.2009

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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\paper Non-Hermitian spin chains with inhomogeneous coupling
\jour Algebra i Analiz
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\pages 80--106
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\jour St. Petersburg Math. J.
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\pages 393--410
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Bytsko A., “Tensor Space Representations of Temperley-Lieb Algebra Via Orthogonal Projections of Rank R >= 1”, J. Math. Phys., 56:8 (2015), 083502  crossref  mathscinet  zmath  isi  scopus
    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  crossref  isi  elib  scopus
    4. Viennot D., Aubourg L., “Quantum Chimera States”, Phys. Lett. A, 380:5-6 (2016), 678–683  crossref  mathscinet  isi  elib  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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