Ghent University Academic Bibliography

Advanced

An exactly solvable spin chain related to Hahn polynomials

Nedialka Stoilova UGent and Joris Van der Jeugt UGent (2011) SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 7.
abstract
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Quantum communication, perfect state transfer, Hahn polynomials
journal title
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
Symmetry Integr. Geom.
volume
7
article number
033
pages
13 pages
Web of Science type
Article
Web of Science id
000288846600001
JCR category
PHYSICS, MATHEMATICAL
JCR impact factor
1.071 (2011)
JCR rank
33/55 (2011)
JCR quartile
3 (2011)
ISSN
1815-0659
DOI
10.3842/SIGMA.2011.033
language
English
UGent publication?
yes
classification
A1
copyright statement
I don't know the status of the copyright for this publication
id
1204699
handle
http://hdl.handle.net/1854/LU-1204699
date created
2011-04-08 08:45:59
date last changed
2016-12-21 15:42:26
@article{1204699,
  abstract     = {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 \ensuremath{\alpha} and depends on the parity of the chain site. Extending the model by a second parameter \ensuremath{\beta}, 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 (\ensuremath{\alpha},\ensuremath{\beta}) and (\ensuremath{\alpha}+1,\ensuremath{\beta}\ensuremath{-}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.},
  articleno    = {033},
  author       = {Stoilova, Nedialka and Van der Jeugt, Joris},
  issn         = {1815-0659},
  journal      = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
  keyword      = {Quantum communication,perfect state transfer,Hahn polynomials},
  language     = {eng},
  pages        = {13},
  title        = {An exactly solvable spin chain related to Hahn polynomials},
  url          = {http://dx.doi.org/10.3842/SIGMA.2011.033},
  volume       = {7},
  year         = {2011},
}

Chicago
Stoilova, Nedialka, and Joris Van der Jeugt. 2011. “An Exactly Solvable Spin Chain Related to Hahn Polynomials.” Symmetry Integrability and Geometry-methods and Applications 7.
APA
Stoilova, Nedialka, & Van der Jeugt, J. (2011). An exactly solvable spin chain related to Hahn polynomials. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 7.
Vancouver
1.
Stoilova N, Van der Jeugt J. An exactly solvable spin chain related to Hahn polynomials. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 2011;7.
MLA
Stoilova, Nedialka, and Joris Van der Jeugt. “An Exactly Solvable Spin Chain Related to Hahn Polynomials.” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 7 (2011): n. pag. Print.