An Exactly Solvable Spin Chain Related to Hahn Polynomials
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
An Exactly Solvable Spin Chain Related to Hahn Polynomials
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| Creator |
Stoilova, N.I.
Van der Jeugt, J. |
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| 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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| Date |
2019-02-11T15:27:39Z
2019-02-11T15:27:39Z 2011 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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