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TMF, 2008, Volume 155, Number 1, Pages 94–108 (Mi tmf6195)  

This article is cited in 2 scientific papers (total in 2 papers)

Eigenvectors of the Baxter–Bazhanov–Stroganov $\tau^{(2)}(t_q)$ model with fixed-spin boundary conditions

N. Z. Iorgov, V. N. Shadura, Yu. V. Tykhyy

N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine

Abstract: We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter–Bazhanov–Stroganov {(}BBS{\rm)} model {\rm(}$N$-state spin model{\rm)} with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin's method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding $T$$Q$ Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like $\mathbb{Z}_N$ quantum chain model.

Keywords: integrable quantum chain, fixed boundary conditions, method of separation of variables

DOI: https://doi.org/10.4213/tmf6195

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English version:
Theoretical and Mathematical Physics, 2008, 155:1, 585–597

Bibliographic databases:

Received: 31.03.2008

Citation: N. Z. Iorgov, V. N. Shadura, Yu. V. Tykhyy, “Eigenvectors of the Baxter–Bazhanov–Stroganov $\tau^{(2)}(t_q)$ model with fixed-spin boundary conditions”, TMF, 155:1 (2008), 94–108; Theoret. and Math. Phys., 155:1 (2008), 585–597

Citation in format AMSBIB
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\paper Eigenvectors of the Baxter--Bazhanov--Stroganov $\tau^{(2)}(t_q)$
model with fixed-spin boundary conditions
\jour TMF
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\pages 94--108
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\crossref{https://doi.org/10.4213/tmf6195}
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\jour Theoret. and Math. Phys.
\yr 2008
\vol 155
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\pages 585--597
\crossref{https://doi.org/10.1007/s11232-008-0048-1}
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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. von Gehlen G., Iorgov N., Pakuliak S., Shadura V., “Factorized finite-size Ising model spin matrix elements from separation of variables”, J. Phys. A, 42:30 (2009), 304026, 28 pp.  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Au-Yang H., Perk J.H.H., “Identities in the superintegrable chiral Potts model”, J. Phys. A, 43:2 (2010), 025203, 10 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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