Entropy and modular Hamiltonian for a free chiral scalar in two intervals

Autores
Arias, Raúl Eduardo; Casini, Horacio German; Huerta, Marina; Pontello, Diego Esteban
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current j(x)=∂φ(x) corresponding to a chiral free scalar φ in d=2. We also compute explicitly the mutual information between the intervals. This model shows a failure of Haag duality for two intervals that translates into a loss of a symmetry property for the mutual information usually associated with modular invariance. Contrary to the case of a free massless fermion, the modular Hamiltonian turns out to be completely nonlocal. The calculation is done diagonalizing the density matrix by computing the eigensystem of a correlator kernel operator. These eigenvectors are obtained by a novel method that involves solving an equivalent problem for a holomorphic function in the complex plane where multiplicative boundary conditions are imposed on the intervals. Using the same technique we also rederive the free fermion modular Hamiltonian in a more transparent way.
Fil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Huerta, Marina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pontello, Diego Esteban. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
MODULAR
ENTANGLEMENT
ENTROPY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/102620
Acceder
id CONICETDig_a28f4daa89accc2186c1a44537bccba4
oai_identifier_str oai:ri.conicet.gov.ar:11336/102620
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Entropy and modular Hamiltonian for a free chiral scalar in two intervalsArias, Raúl EduardoCasini, Horacio GermanHuerta, MarinaPontello, Diego EstebanMODULARENTANGLEMENTENTROPYhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current j(x)=∂φ(x) corresponding to a chiral free scalar φ in d=2. We also compute explicitly the mutual information between the intervals. This model shows a failure of Haag duality for two intervals that translates into a loss of a symmetry property for the mutual information usually associated with modular invariance. Contrary to the case of a free massless fermion, the modular Hamiltonian turns out to be completely nonlocal. The calculation is done diagonalizing the density matrix by computing the eigensystem of a correlator kernel operator. These eigenvectors are obtained by a novel method that involves solving an equivalent problem for a holomorphic function in the complex plane where multiplicative boundary conditions are imposed on the intervals. Using the same technique we also rederive the free fermion modular Hamiltonian in a more transparent way.Fil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Huerta, Marina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pontello, Diego Esteban. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Physical Society2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/102620Arias, Raúl Eduardo; Casini, Horacio German; Huerta, Marina; Pontello, Diego Esteban; Entropy and modular Hamiltonian for a free chiral scalar in two intervals; American Physical Society; Physical Review D; 98; 12; 12-2018; 1-31; 1250082470-0010CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.98.125008info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.98.125008info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1809.00026info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:05:33Zoai:ri.conicet.gov.ar:11336/102620instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:05:33.987CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Entropy and modular Hamiltonian for a free chiral scalar in two intervals
title Entropy and modular Hamiltonian for a free chiral scalar in two intervals
spellingShingle Entropy and modular Hamiltonian for a free chiral scalar in two intervals
Arias, Raúl Eduardo
MODULAR
ENTANGLEMENT
ENTROPY
title_short Entropy and modular Hamiltonian for a free chiral scalar in two intervals
title_full Entropy and modular Hamiltonian for a free chiral scalar in two intervals
title_fullStr Entropy and modular Hamiltonian for a free chiral scalar in two intervals
title_full_unstemmed Entropy and modular Hamiltonian for a free chiral scalar in two intervals
title_sort Entropy and modular Hamiltonian for a free chiral scalar in two intervals
dc.creator.none.fl_str_mv Arias, Raúl Eduardo
Casini, Horacio German
Huerta, Marina
Pontello, Diego Esteban
author Arias, Raúl Eduardo
author_facet Arias, Raúl Eduardo
Casini, Horacio German
Huerta, Marina
Pontello, Diego Esteban
author_role author
author2 Casini, Horacio German
Huerta, Marina
Pontello, Diego Esteban
author2_role author
author
author
dc.subject.none.fl_str_mv MODULAR
ENTANGLEMENT
ENTROPY
topic MODULAR
ENTANGLEMENT
ENTROPY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current j(x)=∂φ(x) corresponding to a chiral free scalar φ in d=2. We also compute explicitly the mutual information between the intervals. This model shows a failure of Haag duality for two intervals that translates into a loss of a symmetry property for the mutual information usually associated with modular invariance. Contrary to the case of a free massless fermion, the modular Hamiltonian turns out to be completely nonlocal. The calculation is done diagonalizing the density matrix by computing the eigensystem of a correlator kernel operator. These eigenvectors are obtained by a novel method that involves solving an equivalent problem for a holomorphic function in the complex plane where multiplicative boundary conditions are imposed on the intervals. Using the same technique we also rederive the free fermion modular Hamiltonian in a more transparent way.
Fil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Huerta, Marina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pontello, Diego Esteban. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current j(x)=∂φ(x) corresponding to a chiral free scalar φ in d=2. We also compute explicitly the mutual information between the intervals. This model shows a failure of Haag duality for two intervals that translates into a loss of a symmetry property for the mutual information usually associated with modular invariance. Contrary to the case of a free massless fermion, the modular Hamiltonian turns out to be completely nonlocal. The calculation is done diagonalizing the density matrix by computing the eigensystem of a correlator kernel operator. These eigenvectors are obtained by a novel method that involves solving an equivalent problem for a holomorphic function in the complex plane where multiplicative boundary conditions are imposed on the intervals. Using the same technique we also rederive the free fermion modular Hamiltonian in a more transparent way.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/102620
Arias, Raúl Eduardo; Casini, Horacio German; Huerta, Marina; Pontello, Diego Esteban; Entropy and modular Hamiltonian for a free chiral scalar in two intervals; American Physical Society; Physical Review D; 98; 12; 12-2018; 1-31; 125008
2470-0010
CONICET Digital
CONICET
url http://hdl.handle.net/11336/102620
identifier_str_mv Arias, Raúl Eduardo; Casini, Horacio German; Huerta, Marina; Pontello, Diego Esteban; Entropy and modular Hamiltonian for a free chiral scalar in two intervals; American Physical Society; Physical Review D; 98; 12; 12-2018; 1-31; 125008
2470-0010
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.98.125008
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.98.125008
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1809.00026
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
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:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842980208370515968
score 12.993085

Publicaciones similares