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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146802 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862556688324755456 |
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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.
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| first_indexed | 2025-11-25T22:33:36Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146802 |
| 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 |
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| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Exactly Solvable Spin Chain Related to Hahn Polynomials Article published earlier |
| 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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