Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/73356 |
Resumo: | Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S (k,ω) and S (k,ω)=S (k,ω). The contribution of Bethe strings to S (k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S (k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S (k,ω), S (k,ω)=S (k,ω), and S (k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities. +− xx yy zz −+ +− xx yy zz |
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Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chainCiências Naturais::Ciências FísicasScience & TechnologyRecently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S (k,ω) and S (k,ω)=S (k,ω). The contribution of Bethe strings to S (k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S (k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S (k,ω), S (k,ω)=S (k,ω), and S (k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities. +− xx yy zz −+ +− xx yy zzJ. M. P. C. would like to thank the Boston University's Condensed Matter Theory Visitors Program for support and Boston University for hospitality during the initial period of this research. He acknowledges the support from FCT through the Grants PTDC/FIS-MAC/29291/2017, SFRH/BSAB/142925/2018, and POCI-01-0145-FEDER-028887. J. M. P. C. and T. Č. acknowledge the support from FCT through the Grant UID/FIS/04650/2013. T. Č. gratefully acknowledges the support by the Institute for Basic Science in Korea (IBS-R024-D1). P. D. S. acknowledges the support from FCT through the Grants UID/CTM/04540/2013 and UID/CTM/04540/2019.ElsevierUniversidade do MinhoCarmelo, José Manuel PereiraČadež, TilenSacramento, Pedro D.20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/73356engCarmelo, J. M. P., Čadež, T., & Sacramento, P. D. (2020). Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain. Nuclear Physics B, 960, 115175. doi: https://doi.org/10.1016/j.nuclphysb.2020.1151750550-321310.1016/j.nuclphysb.2020.115175https://www.sciencedirect.com/science/article/pii/S0550321320302613info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:07:24Zoai:repositorium.sdum.uminho.pt:1822/73356Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:58:23.214732Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
title |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
spellingShingle |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain Carmelo, José Manuel Pereira Ciências Naturais::Ciências Físicas Science & Technology |
title_short |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
title_full |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
title_fullStr |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
title_full_unstemmed |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
title_sort |
Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain |
author |
Carmelo, José Manuel Pereira |
author_facet |
Carmelo, José Manuel Pereira Čadež, Tilen Sacramento, Pedro D. |
author_role |
author |
author2 |
Čadež, Tilen Sacramento, Pedro D. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Carmelo, José Manuel Pereira Čadež, Tilen Sacramento, Pedro D. |
dc.subject.por.fl_str_mv |
Ciências Naturais::Ciências Físicas Science & Technology |
topic |
Ciências Naturais::Ciências Físicas Science & Technology |
description |
Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S (k,ω) and S (k,ω)=S (k,ω). The contribution of Bethe strings to S (k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S (k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S (k,ω), S (k,ω)=S (k,ω), and S (k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities. +− xx yy zz −+ +− xx yy zz |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020 2020-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/73356 |
url |
http://hdl.handle.net/1822/73356 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Carmelo, J. M. P., Čadež, T., & Sacramento, P. D. (2020). Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain. Nuclear Physics B, 960, 115175. doi: https://doi.org/10.1016/j.nuclphysb.2020.115175 0550-3213 10.1016/j.nuclphysb.2020.115175 https://www.sciencedirect.com/science/article/pii/S0550321320302613 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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