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Remarks towards the spectrum of the Heisenberg spin chain type models

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Abstract

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model (“small polaron model”) is considered. Finally, we discuss some questions relating to the general open Hecke chain models.

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, 141980, Russia

    J. Fuksa, A. P. Isaev & S. O. Krivonos

  2. Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague, Prague, Czech Republic

    Č. Burdík & J. Fuksa

  3. Department of Mathematics, Faculty of Transportation Sciences Czech Technical University in Prague, Prague, Czech Republic

    O. Navrátil

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  1. Č. Burdík
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  2. J. Fuksa
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  3. A. P. Isaev
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  4. S. O. Krivonos
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  5. O. Navrátil
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Correspondence to Č. Burdík.

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Burdík, Č., Fuksa, J., Isaev, A.P. et al. Remarks towards the spectrum of the Heisenberg spin chain type models. Phys. Part. Nuclei 46, 277–309 (2015). https://doi.org/10.1134/S1063779615030053

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