Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture

We compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In...

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Detalles Bibliográficos
Autores: Barba, J. C:, Finkel Morgenstern, Federico, González López, Artemio, Rodríguez González, Miguel Ángel
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/51490
Acceso en línea:https://hdl.handle.net/20.500.14352/51490
Access Level:acceso abierto
Palabra clave:51-73
Física-Modelos matemáticos
Física matemática
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spelling Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjectureBarba, J. C:Finkel Morgenstern, FedericoGonzález López, ArtemioRodríguez González, Miguel Ángel51-73Física-Modelos matemáticosFísica matemáticaWe compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of (normalized) spacings between consecutive levels is of neither Poisson nor Wigner type but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models since they do not satisfy a well-known conjecture of Berry and Tabor, according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC_N-type Polychronakos-Frahm chain using only a few essential properties of its spectrum such as the Gaussian character of the level density and the fact that the energy levels are equally spaced. This expression is shown to be in excellent agreement with the numerical data.American Physical SocietyUniversidad Complutense de Madrid20082008-06-0120082008-06-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/51490reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/514902026-06-02T12:44:21Z
dc.title.none.fl_str_mv Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
title Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
spellingShingle Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
Barba, J. C:
51-73
Física-Modelos matemáticos
Física matemática
title_short Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
title_full Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
title_fullStr Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
title_full_unstemmed Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
title_sort Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
dc.creator.none.fl_str_mv Barba, J. C:
Finkel Morgenstern, Federico
González López, Artemio
Rodríguez González, Miguel Ángel
author Barba, J. C:
author_facet Barba, J. C:
Finkel Morgenstern, Federico
González López, Artemio
Rodríguez González, Miguel Ángel
author_role author
author2 Finkel Morgenstern, Federico
González López, Artemio
Rodríguez González, Miguel Ángel
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Física-Modelos matemáticos
Física matemática
topic 51-73
Física-Modelos matemáticos
Física matemática
description We compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of (normalized) spacings between consecutive levels is of neither Poisson nor Wigner type but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models since they do not satisfy a well-known conjecture of Berry and Tabor, according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC_N-type Polychronakos-Frahm chain using only a few essential properties of its spectrum such as the Gaussian character of the level density and the fact that the energy levels are equally spaced. This expression is shown to be in excellent agreement with the numerical data.
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-06-01
2008
2008-06-01
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/20.500.14352/51490
url https://hdl.handle.net/20.500.14352/51490
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 American Physical Society
publisher.none.fl_str_mv American Physical Society
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
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score 15,301603

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