Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices

Autores
Zemba, Guillermo Raúl
Año de publicación
2026
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Zemba, Guillermo Raúl. Facultad de Ciencias Fisicomatemáticas e Ingeniería. Pontificia Universidad Católica Argentina; Argentina
Free gases of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds Rd/Γ , where Γ is the crystallographic group of symmetry in d-dimensional momentum space, are used to accomplish this task. Two topological classes exist for d=1 : an interval, which is identified as a conductor, and a circumference, which corresponds to an insulator. The number of topological classes increases to 17 for d=2 : 8 have the topology of a disk, that are generally recognized as conductors, and 4 correspond to a two-sphere, matching insulators. Both sets eventually contain a finite number of conical singularities and reflection corners at the boundaries. The remaining cases in the listing relate to conductors (annulus, Möbius strip) and insulators (two-torus, real projective plane, Klein bottle). Examples that fall under this list are given, along with physical interpretations of the singularities. It is anticipated that the findings of this classification will be robust under perturbative interactions due to its topological character.
Fuente
Mathematics, 14(2), 303
Materia
PARTICULAS LIBRES
MAR DE FERMI
FISICA
MATEMATICA
FERMION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
Repositorio Institucional (UCA)
Institución
Pontificia Universidad Católica Argentina
OAI Identificador
oai:ucacris:123456789/21883
Acceder
id RIUCA_916eaae1570d4e36fd223b1e524ffffb
oai_identifier_str oai:ucacris:123456789/21883
network_acronym_str RIUCA
repository_id_str 2585
network_name_str Repositorio Institucional (UCA)
spelling Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional LatticesZemba, Guillermo RaúlPARTICULAS LIBRESMAR DE FERMIFISICAMATEMATICAFERMIONFil: Zemba, Guillermo Raúl. Facultad de Ciencias Fisicomatemáticas e Ingeniería. Pontificia Universidad Católica Argentina; ArgentinaFree gases of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds Rd/Γ , where Γ is the crystallographic group of symmetry in d-dimensional momentum space, are used to accomplish this task. Two topological classes exist for d=1 : an interval, which is identified as a conductor, and a circumference, which corresponds to an insulator. The number of topological classes increases to 17 for d=2 : 8 have the topology of a disk, that are generally recognized as conductors, and 4 correspond to a two-sphere, matching insulators. Both sets eventually contain a finite number of conical singularities and reflection corners at the boundaries. The remaining cases in the listing relate to conductors (annulus, Möbius strip) and insulators (two-torus, real projective plane, Klein bottle). Examples that fall under this list are given, along with physical interpretations of the singularities. It is anticipated that the findings of this classification will be robust under perturbative interactions due to its topological character.MDPI2026info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttps://repositorio.uca.edu.ar/handle/123456789/218832227-7390https://doi.org/10.3390/math14020303Mathematics, 14(2), 303reponame:Repositorio Institucional (UCA)instname:Pontificia Universidad Católica Argentinaenginfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/4.0/2026-09-28T11:10:43Zoai:ucacris:123456789/21883instacron:UCAInstitucionalhttps://repositorio.uca.edu.ar/Universidad privadaNo correspondehttps://repositorio.uca.edu.ar/oaiclaudia_fernandez@uca.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:25852026-09-28 11:10:43.686Repositorio Institucional (UCA) - Pontificia Universidad Católica Argentinafalse
dc.title.none.fl_str_mv Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
title Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
spellingShingle Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
Zemba, Guillermo Raúl
PARTICULAS LIBRES
MAR DE FERMI
FISICA
MATEMATICA
FERMION
title_short Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
title_full Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
title_fullStr Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
title_full_unstemmed Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
title_sort Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
dc.creator.none.fl_str_mv Zemba, Guillermo Raúl
author Zemba, Guillermo Raúl
author_facet Zemba, Guillermo Raúl
author_role author
dc.subject.none.fl_str_mv PARTICULAS LIBRES
MAR DE FERMI
FISICA
MATEMATICA
FERMION
topic PARTICULAS LIBRES
MAR DE FERMI
FISICA
MATEMATICA
FERMION
dc.description.none.fl_txt_mv Fil: Zemba, Guillermo Raúl. Facultad de Ciencias Fisicomatemáticas e Ingeniería. Pontificia Universidad Católica Argentina; Argentina
Free gases of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds Rd/Γ , where Γ is the crystallographic group of symmetry in d-dimensional momentum space, are used to accomplish this task. Two topological classes exist for d=1 : an interval, which is identified as a conductor, and a circumference, which corresponds to an insulator. The number of topological classes increases to 17 for d=2 : 8 have the topology of a disk, that are generally recognized as conductors, and 4 correspond to a two-sphere, matching insulators. Both sets eventually contain a finite number of conical singularities and reflection corners at the boundaries. The remaining cases in the listing relate to conductors (annulus, Möbius strip) and insulators (two-torus, real projective plane, Klein bottle). Examples that fall under this list are given, along with physical interpretations of the singularities. It is anticipated that the findings of this classification will be robust under perturbative interactions due to its topological character.
description Fil: Zemba, Guillermo Raúl. Facultad de Ciencias Fisicomatemáticas e Ingeniería. Pontificia Universidad Católica Argentina; Argentina
publishDate 2026
dc.date.none.fl_str_mv 2026
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 https://repositorio.uca.edu.ar/handle/123456789/21883
2227-7390
https://doi.org/10.3390/math14020303
url https://repositorio.uca.edu.ar/handle/123456789/21883
https://doi.org/10.3390/math14020303
identifier_str_mv 2227-7390
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv Mathematics, 14(2), 303
reponame:Repositorio Institucional (UCA)
instname:Pontificia Universidad Católica Argentina
reponame_str Repositorio Institucional (UCA)
collection Repositorio Institucional (UCA)
instname_str Pontificia Universidad Católica Argentina
repository.name.fl_str_mv Repositorio Institucional (UCA) - Pontificia Universidad Católica Argentina
repository.mail.fl_str_mv claudia_fernandez@uca.edu.ar
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score 13.265058

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