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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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146802 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146802 |
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irk-123456789-1468022019-02-12T01:24:14Z An Exactly Solvable Spin Chain Related to Hahn Polynomials Stoilova, N.I. Van der Jeugt, J. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146802 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Stoilova, N.I. Van der Jeugt, J. |
| spellingShingle |
Stoilova, N.I. Van der Jeugt, J. An Exactly Solvable Spin Chain Related to Hahn Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Stoilova, N.I. Van der Jeugt, J. |
| author_sort |
Stoilova, N.I. |
| title |
An Exactly Solvable Spin Chain Related to Hahn Polynomials |
| title_short |
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_sort |
exactly solvable spin chain related to hahn polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146802 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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