Exact analytical solution of a time-reversal-invariant topological superconducting wire

Autores
Aligia, Armando Angel; Camjayi, Alberto
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a model proposed before for a time-reversal-invariant topological superconductor which contains a hopping term t, a chemical potential μ, an extended s-wave pairing Δ, and spin-orbit coupling λ. We show that for |Δ|=|λ|, μ=t=0, the model has an exact analytical solution defining new fermion operators involving nearest-neighbor sites. The many-body ground state is fourfold degenerate due to the existence of two zero-energy modes localized exactly at the first and last sites of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results, we discuss some statements related to the so-called time-reversal anomaly. The addition of a small hopping term t for a chain with an even number of sites breaks the degeneracy, and the ground state becomes unique with an even number of particles. We also consider a small magnetic field B applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains obtained treating t and B as small perturbations with numerical results in a short chain, obtaining good agreement.
Fil: Aligia, Armando Angel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Camjayi, Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Materia
SUPERCONDUCTOR
TOPOLOGICAL
EXACT
SOLUTION
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:11336/147416
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Exact analytical solution of a time-reversal-invariant topological superconducting wireAligia, Armando AngelCamjayi, AlbertoSUPERCONDUCTORTOPOLOGICALEXACTSOLUTIONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We consider a model proposed before for a time-reversal-invariant topological superconductor which contains a hopping term t, a chemical potential μ, an extended s-wave pairing Δ, and spin-orbit coupling λ. We show that for |Δ|=|λ|, μ=t=0, the model has an exact analytical solution defining new fermion operators involving nearest-neighbor sites. The many-body ground state is fourfold degenerate due to the existence of two zero-energy modes localized exactly at the first and last sites of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results, we discuss some statements related to the so-called time-reversal anomaly. The addition of a small hopping term t for a chain with an even number of sites breaks the degeneracy, and the ground state becomes unique with an even number of particles. We also consider a small magnetic field B applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains obtained treating t and B as small perturbations with numerical results in a short chain, obtaining good agreement.Fil: Aligia, Armando Angel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Camjayi, Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaAmerican Physical Society2019-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/147416Aligia, Armando Angel; Camjayi, Alberto; Exact analytical solution of a time-reversal-invariant topological superconducting wire; American Physical Society; Physical Review B; 100; 11; 9-20192469-9969CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevB.100.115413info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevB.100.115413info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1905.04255info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:16:13Zoai:ri.conicet.gov.ar:11336/147416instacron: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:34982025-11-05 10:16:13.634CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Exact analytical solution of a time-reversal-invariant topological superconducting wire
title Exact analytical solution of a time-reversal-invariant topological superconducting wire
spellingShingle Exact analytical solution of a time-reversal-invariant topological superconducting wire
Aligia, Armando Angel
SUPERCONDUCTOR
TOPOLOGICAL
EXACT
SOLUTION
title_short Exact analytical solution of a time-reversal-invariant topological superconducting wire
title_full Exact analytical solution of a time-reversal-invariant topological superconducting wire
title_fullStr Exact analytical solution of a time-reversal-invariant topological superconducting wire
title_full_unstemmed Exact analytical solution of a time-reversal-invariant topological superconducting wire
title_sort Exact analytical solution of a time-reversal-invariant topological superconducting wire
dc.creator.none.fl_str_mv Aligia, Armando Angel
Camjayi, Alberto
author Aligia, Armando Angel
author_facet Aligia, Armando Angel
Camjayi, Alberto
author_role author
author2 Camjayi, Alberto
author2_role author
dc.subject.none.fl_str_mv SUPERCONDUCTOR
TOPOLOGICAL
EXACT
SOLUTION
topic SUPERCONDUCTOR
TOPOLOGICAL
EXACT
SOLUTION
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 consider a model proposed before for a time-reversal-invariant topological superconductor which contains a hopping term t, a chemical potential μ, an extended s-wave pairing Δ, and spin-orbit coupling λ. We show that for |Δ|=|λ|, μ=t=0, the model has an exact analytical solution defining new fermion operators involving nearest-neighbor sites. The many-body ground state is fourfold degenerate due to the existence of two zero-energy modes localized exactly at the first and last sites of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results, we discuss some statements related to the so-called time-reversal anomaly. The addition of a small hopping term t for a chain with an even number of sites breaks the degeneracy, and the ground state becomes unique with an even number of particles. We also consider a small magnetic field B applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains obtained treating t and B as small perturbations with numerical results in a short chain, obtaining good agreement.
Fil: Aligia, Armando Angel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Camjayi, Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
description We consider a model proposed before for a time-reversal-invariant topological superconductor which contains a hopping term t, a chemical potential μ, an extended s-wave pairing Δ, and spin-orbit coupling λ. We show that for |Δ|=|λ|, μ=t=0, the model has an exact analytical solution defining new fermion operators involving nearest-neighbor sites. The many-body ground state is fourfold degenerate due to the existence of two zero-energy modes localized exactly at the first and last sites of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results, we discuss some statements related to the so-called time-reversal anomaly. The addition of a small hopping term t for a chain with an even number of sites breaks the degeneracy, and the ground state becomes unique with an even number of particles. We also consider a small magnetic field B applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains obtained treating t and B as small perturbations with numerical results in a short chain, obtaining good agreement.
publishDate 2019
dc.date.none.fl_str_mv 2019-09
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/11336/147416
Aligia, Armando Angel; Camjayi, Alberto; Exact analytical solution of a time-reversal-invariant topological superconducting wire; American Physical Society; Physical Review B; 100; 11; 9-2019
2469-9969
CONICET Digital
CONICET
url http://hdl.handle.net/11336/147416
identifier_str_mv Aligia, Armando Angel; Camjayi, Alberto; Exact analytical solution of a time-reversal-invariant topological superconducting wire; American Physical Society; Physical Review B; 100; 11; 9-2019
2469-9969
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/PhysRevB.100.115413
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevB.100.115413
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1905.04255
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
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
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score 13.082534

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