Anyon-Hubbard model in optical lattices
Abstract. Anyons can be considered to be a third class of particles with nontrivial exchange statistics that interpolate between fermions and bosons (they do not obey Bose-Einstein or Fermi-Dirac statistics). For two anyons under particle exchange, the wave function acquires a fractional phase e^(iθ...
- Autores:
-
Arcila Forero, Julian Felipe
- Tipo de recurso:
- Fecha de publicación:
- 2017
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/62026
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/62026
http://bdigital.unal.edu.co/60866/
- Palabra clave:
- 0 Generalidades / Computer science, information and general works
53 Física / Physics
Anyons
One-dimension
Optical lattice
Hubbard model
DMRG
Aniones
Una dimensión
Redes ópticas
Modelo -Hubbard
Transición cuántica
Entrelazamiento
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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dc.title.spa.fl_str_mv |
Anyon-Hubbard model in optical lattices |
title |
Anyon-Hubbard model in optical lattices |
spellingShingle |
Anyon-Hubbard model in optical lattices 0 Generalidades / Computer science, information and general works 53 Física / Physics Anyons One-dimension Optical lattice Hubbard model DMRG Aniones Una dimensión Redes ópticas Modelo -Hubbard Transición cuántica Entrelazamiento |
title_short |
Anyon-Hubbard model in optical lattices |
title_full |
Anyon-Hubbard model in optical lattices |
title_fullStr |
Anyon-Hubbard model in optical lattices |
title_full_unstemmed |
Anyon-Hubbard model in optical lattices |
title_sort |
Anyon-Hubbard model in optical lattices |
dc.creator.fl_str_mv |
Arcila Forero, Julian Felipe |
dc.contributor.author.spa.fl_str_mv |
Arcila Forero, Julian Felipe |
dc.contributor.spa.fl_str_mv |
Silva Valencia, Jereson |
dc.subject.ddc.spa.fl_str_mv |
0 Generalidades / Computer science, information and general works 53 Física / Physics |
topic |
0 Generalidades / Computer science, information and general works 53 Física / Physics Anyons One-dimension Optical lattice Hubbard model DMRG Aniones Una dimensión Redes ópticas Modelo -Hubbard Transición cuántica Entrelazamiento |
dc.subject.proposal.spa.fl_str_mv |
Anyons One-dimension Optical lattice Hubbard model DMRG Aniones Una dimensión Redes ópticas Modelo -Hubbard Transición cuántica Entrelazamiento |
description |
Abstract. Anyons can be considered to be a third class of particles with nontrivial exchange statistics that interpolate between fermions and bosons (they do not obey Bose-Einstein or Fermi-Dirac statistics). For two anyons under particle exchange, the wave function acquires a fractional phase e^(iθ) , giving rise to fractional statistics with 0 θ π. We study the properties of a collective of anyons loaded in an one-dimensional optical lattice at a zero temperature. We study a Hubbard model of anyons that takes into account the hopping of the particles along the lattice and the local two-body interaction between them. With the aim to proposing a realistic setup, Keilmann et al. introduces an exact mapping between anyons and bosons in one-dimension (the fractional version of the Jordan-Wigner transformation) [1]. We used this exact mapping and we studied the anyon-Hubbard Hamitonian in terms of bosonic operators. Thus, the model is a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle (t → te^{iθn_j} ). The study was performed by means of the density matrix renormalization group (DMRG), which has allowed us to obtain the phase diagram for different values of the statistical angle θ and densities ρ = N/L. We observe the gapped (Mott insulator) and gapless (superfluid) phases that characterized the phase diagram and we calculated these phase diagram for higher densities. The phase transition was studied using the block von Neumman entropy, and we were able to observe the superfluid to Mott insulator transition. In particular, we use the estimator proposed by Lauchli and Kollath to determine the critical points, which has enabled us to present the evolution of the critical point with the global density and the statistical angle. On the other hand, when we change the local interaction in the system, anyons interacting via repulsive local three-body interactions, the quantum phase transition is driven by the statistics and the appearence of Mott insulator states, for the system with ρ = 1, depends on the anyonic angle. We showed the phases diagram and it was possible to study the influence of the many-body interactions on critical point position. |
publishDate |
2017 |
dc.date.issued.spa.fl_str_mv |
2017-07 |
dc.date.accessioned.spa.fl_str_mv |
2019-07-02T20:49:27Z |
dc.date.available.spa.fl_str_mv |
2019-07-02T20:49:27Z |
dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
status_str |
acceptedVersion |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/62026 |
dc.identifier.eprints.spa.fl_str_mv |
http://bdigital.unal.edu.co/60866/ |
url |
https://repositorio.unal.edu.co/handle/unal/62026 http://bdigital.unal.edu.co/60866/ |
dc.language.iso.spa.fl_str_mv |
spa |
language |
spa |
dc.relation.spa.fl_str_mv |
http://ciencias.bogota.unal.edu.co/gruposdeinvestigacion/grupo-de-sistemas-correlacionados/?L=1 |
dc.relation.ispartof.spa.fl_str_mv |
Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Física Departamento de Física |
dc.relation.references.spa.fl_str_mv |
Arcila Forero, Julian Felipe (2017) Anyon-Hubbard model in optical lattices. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá. |
dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
dc.rights.license.spa.fl_str_mv |
Atribución-NoComercial 4.0 Internacional |
dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc/4.0/ |
dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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application/pdf |
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Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/bitstream/unal/62026/1/1024493947_2017.pdf https://repositorio.unal.edu.co/bitstream/unal/62026/2/1024493947_2017.pdf.jpg |
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spelling |
Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Silva Valencia, JeresonArcila Forero, Julian Felipe55de1e40-56ea-42fc-bf86-72c77a85c6753002019-07-02T20:49:27Z2019-07-02T20:49:27Z2017-07https://repositorio.unal.edu.co/handle/unal/62026http://bdigital.unal.edu.co/60866/Abstract. Anyons can be considered to be a third class of particles with nontrivial exchange statistics that interpolate between fermions and bosons (they do not obey Bose-Einstein or Fermi-Dirac statistics). For two anyons under particle exchange, the wave function acquires a fractional phase e^(iθ) , giving rise to fractional statistics with 0 θ π. We study the properties of a collective of anyons loaded in an one-dimensional optical lattice at a zero temperature. We study a Hubbard model of anyons that takes into account the hopping of the particles along the lattice and the local two-body interaction between them. With the aim to proposing a realistic setup, Keilmann et al. introduces an exact mapping between anyons and bosons in one-dimension (the fractional version of the Jordan-Wigner transformation) [1]. We used this exact mapping and we studied the anyon-Hubbard Hamitonian in terms of bosonic operators. Thus, the model is a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle (t → te^{iθn_j} ). The study was performed by means of the density matrix renormalization group (DMRG), which has allowed us to obtain the phase diagram for different values of the statistical angle θ and densities ρ = N/L. We observe the gapped (Mott insulator) and gapless (superfluid) phases that characterized the phase diagram and we calculated these phase diagram for higher densities. The phase transition was studied using the block von Neumman entropy, and we were able to observe the superfluid to Mott insulator transition. In particular, we use the estimator proposed by Lauchli and Kollath to determine the critical points, which has enabled us to present the evolution of the critical point with the global density and the statistical angle. On the other hand, when we change the local interaction in the system, anyons interacting via repulsive local three-body interactions, the quantum phase transition is driven by the statistics and the appearence of Mott insulator states, for the system with ρ = 1, depends on the anyonic angle. We showed the phases diagram and it was possible to study the influence of the many-body interactions on critical point position.Los aniones pueden ser considerados como una tercera categoría de partículas con un una estadística de intercambio no trivial, que interpolan entre fermiones y bosones (no obedecen a las estadísitca de Bose-Einstein ni Fermi-Dirac). Para dos aniones bajo intercambio de partículas, la función de onda adquiere una fase fraccional e iθ, dando lugar a una estadística fraccional con 0 θ π. Nosotros estudiamos la propiedades de una colectivo de aniones cargados en una red óptica unidimensional a temperatura cero. Estudiamos un modelo Hubbard de aniones que tiene en cuenta el salto de las partículas a lo largo de la red y la interacción local de dos cuerpos entre ellas. Con el objetivo de proponer un esquema realístico, Keilmann et al. introducen un mapeo exacto entre aniones y bosones en una dimensión (La versión fraccional de la transformación de Jordan-Wigner). Nosotros usamos este mapeo exacto y estudiamos el Hamiltoniano de anyon-Hubbard en términos de operadores bosónicos. Así, el modelo es una modelo de Bose-Hubbard modificado en donde el tunelamiento depende de la densidad y el ángulo de intercambio (t → teiθ). El estudio se realizó por medio del grupo de renormalización de la matriz densidad (DMRG, por su sigla en inglés), el cual nos permitió obtener los diagramas de fases para diferentes valores del ángulo de la estadística θ y de la densidad ρ = N/L. Nosotros observamos una fase con gap (aislante de Mott) y una fase sin gap (superfluida) que caracteriza a los diagramas de fase y calculamos estos diagramas para altas densidades. La transición de fase fue estudiada usando la entropía de bloque de von Neumann y fue posible observar la transición de superfluido a aislante de Mott. En particular, usamos el estimador propuesto por Läuchli y Kollath para determinar los puntos críticos, lo cual nos permitió presentar la evolución de los puntos críticos con la densidad global y con el ángulo de la estadística. Por otra parte, cuando cambiamos la interacción local en el sistema, aniones interactuando por medio de una interacción repulsiva de tres cuerpos. La transición de fase cuántica es manejada por la estadística y la aparición de estados aislantes de Mott, para el sistema con ρ = 1, dependen del ángulo aniónico. Nosotros mostramos los diagramas de fase y fue posible estudiar la influencia de las interacciones de muchos cuerpos sobre la posición del punto crítico.Maestríaapplication/pdfspahttp://ciencias.bogota.unal.edu.co/gruposdeinvestigacion/grupo-de-sistemas-correlacionados/?L=1Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de FísicaDepartamento de FísicaArcila Forero, Julian Felipe (2017) Anyon-Hubbard model in optical lattices. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.0 Generalidades / Computer science, information and general works53 Física / PhysicsAnyonsOne-dimensionOptical latticeHubbard modelDMRGAnionesUna dimensiónRedes ópticasModelo -HubbardTransición cuánticaEntrelazamientoAnyon-Hubbard model in optical latticesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL1024493947_2017.pdfapplication/pdf1614671https://repositorio.unal.edu.co/bitstream/unal/62026/1/1024493947_2017.pdf16e5dd31f18fdbf5cbc1dd70522d52daMD51THUMBNAIL1024493947_2017.pdf.jpg1024493947_2017.pdf.jpgGenerated Thumbnailimage/jpeg3820https://repositorio.unal.edu.co/bitstream/unal/62026/2/1024493947_2017.pdf.jpga662bf2948e9967b2676301512be6705MD52unal/62026oai:repositorio.unal.edu.co:unal/620262024-04-21 23:51:16.374Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |