A new perspective on the integrability of Inozemtsev's elliptic spin chain

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, for...

Descripción completa

Detalles Bibliográficos
Autores: Finkel Morgenstern, Federico, González López, Artemio
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/34702
Acceso en línea:https://hdl.handle.net/20.500.14352/34702
Access Level:acceso abierto
Palabra clave:51-73
Inverse-square exchange
Long-range interactions
Yangian symmetry
Heisenberg chain
Lie-algebras
Bcn type
N-type
Systems
Model
Spectrum
Física-Modelos matemáticos
Física matemática
id ES_1b71d45c8fbda573f531f6a5ccc4f088
oai_identifier_str oai:docta.ucm.es:20.500.14352/34702
network_acronym_str ES
network_name_str España
repository_id_str
spelling A new perspective on the integrability of Inozemtsev's elliptic spin chainFinkel Morgenstern, FedericoGonzález López, Artemio51-73Inverse-square exchangeLong-range interactionsYangian symmetryHeisenberg chainLie-algebrasBcn typeN-typeSystemsModelSpectrumFísica-Modelos matemáticosFísica matemáticaThe aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane-Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev's chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane-Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane-Shastry chain.Academic Press Inc Elsevier ScienceUniversidad Complutense de Madrid20142014-12-0120142014-12-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/34702reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/347022026-06-02T12:44:21Z
dc.title.none.fl_str_mv A new perspective on the integrability of Inozemtsev's elliptic spin chain
title A new perspective on the integrability of Inozemtsev's elliptic spin chain
spellingShingle A new perspective on the integrability of Inozemtsev's elliptic spin chain
Finkel Morgenstern, Federico
51-73
Inverse-square exchange
Long-range interactions
Yangian symmetry
Heisenberg chain
Lie-algebras
Bcn type
N-type
Systems
Model
Spectrum
Física-Modelos matemáticos
Física matemática
title_short A new perspective on the integrability of Inozemtsev's elliptic spin chain
title_full A new perspective on the integrability of Inozemtsev's elliptic spin chain
title_fullStr A new perspective on the integrability of Inozemtsev's elliptic spin chain
title_full_unstemmed A new perspective on the integrability of Inozemtsev's elliptic spin chain
title_sort A new perspective on the integrability of Inozemtsev's elliptic spin chain
dc.creator.none.fl_str_mv Finkel Morgenstern, Federico
González López, Artemio
author Finkel Morgenstern, Federico
author_facet Finkel Morgenstern, Federico
González López, Artemio
author_role author
author2 González López, Artemio
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Inverse-square exchange
Long-range interactions
Yangian symmetry
Heisenberg chain
Lie-algebras
Bcn type
N-type
Systems
Model
Spectrum
Física-Modelos matemáticos
Física matemática
topic 51-73
Inverse-square exchange
Long-range interactions
Yangian symmetry
Heisenberg chain
Lie-algebras
Bcn type
N-type
Systems
Model
Spectrum
Física-Modelos matemáticos
Física matemática
description The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane-Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev's chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane-Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane-Shastry chain.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-12-01
2014
2014-12-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/34702
url https://hdl.handle.net/20.500.14352/34702
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869404166144655360
score 15.300719

Similares en LA Referencia