An Exactly Solvable Spin Chain Related to Hahn Polynomials

We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, it is shown that the single fermion e...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2011
Main Authors: Stoilova, N.I., Van der Jeugt, J.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146802
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:An Exactly Solvable Spin Chain Related to Hahn Polynomials /N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 22 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Stoilova, N.I.
Van der Jeugt, J.
author_facet Stoilova, N.I.
Van der Jeugt, J.
citation_txt An Exactly Solvable Spin Chain Related to Hahn Polynomials /N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 22 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, 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 (α,β) and (α+1,β−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.
first_indexed 2025-11-25T22:33:36Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-25T22:33:36Z
publishDate 2011
publisher Інститут математики НАН України
record_format dspace
spelling Stoilova, N.I.
Van der Jeugt, J.
2019-02-11T15:27:39Z
2019-02-11T15:27:39Z
2011
An Exactly Solvable Spin Chain Related to Hahn Polynomials /N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 22 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81P45; 33C45
DOI:10.3842/SIGMA.2011.033
https://nasplib.isofts.kiev.ua/handle/123456789/146802
We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, 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 (α,β) and (α+1,β−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.
N.I. Stoilova would like to thank Professor H.D. Doebner (Clausthal, Germany) for constructive discussions. N.I. Stoilova was supported by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy) and by the Humboldt Foundation.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
An Exactly Solvable Spin Chain Related to Hahn Polynomials
Article
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spellingShingle An Exactly Solvable Spin Chain Related to Hahn Polynomials
Stoilova, N.I.
Van der Jeugt, J.
title An Exactly Solvable Spin Chain Related to Hahn Polynomials
title_full An Exactly Solvable Spin Chain Related to Hahn Polynomials
title_fullStr An Exactly Solvable Spin Chain Related to Hahn Polynomials
title_full_unstemmed An Exactly Solvable Spin Chain Related to Hahn Polynomials
title_short An Exactly Solvable Spin Chain Related to Hahn Polynomials
title_sort exactly solvable spin chain related to hahn polynomials
url https://nasplib.isofts.kiev.ua/handle/123456789/146802
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