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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 033, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.033
(Mi sigma591)
 

This article is cited in 15 scientific papers (total in 15 papers)

An Exactly Solvable Spin Chain Related to Hahn Polynomials

Neli I. Stoilovaab, Joris Van der Jeugtb

a Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria
b Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium
References:
Abstract: We study a linear spin chain which was originally introduced by Shi et al. [<i>Phys. Rev. A</i> <b>71</b> (2005), 032309, 5 pages], for which the coupling strength contains a parameter $\alpha$ and depends on the parity of the chain site. Extending the model by a second parameter $\beta$, it is shown that the single fermion eigenstates of the Hamiltonian can be computed in explicit form. The components of these eigenvectors turn out to be Hahn polynomials with parameters $(\alpha,\beta)$ and $(\alpha+1,\beta-1)$. The construction of the eigenvectors relies on two new difference equations for Hahn polynomials. The explicit knowledge of the eigenstates leads to a closed form expression for the correlation function of the spin chain. We also discuss some aspects of a $q$-extension of this model.
Keywords: linear spin chain; Hahn polynomial; state transfer.
Received: January 25, 2011; in final form March 22, 2011; Published online March 29, 2011
Bibliographic databases:
Document Type: Article
MSC: 81P45; 33C45
Language: English
Citation: Neli I. Stoilova, Joris Van der Jeugt, “An Exactly Solvable Spin Chain Related to Hahn Polynomials”, SIGMA, 7 (2011), 033, 13 pp.
Citation in format AMSBIB
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\paper An Exactly Solvable Spin Chain Related to Hahn Polynomials
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  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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