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An Exactly Solvable Spin Chain Related to Hahn Polynomials
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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An Exactly Solvable Spin Chain Related to Hahn Polynomials
Інший ID:
2010 Mathematics Subject Classification: 81P45; 33C45
DOI:10.3842/SIGMA.2011.033
DOI:10.3842/SIGMA.2011.033
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
635
Завантажень:
241
Анотація:
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.
