Modelagem computacional de sistemas de elétrons fortemente correlacionados

Detalhes bibliográficos
Autor(a) principal: Souza, Thiago Xavier Rocha de
Data de Publicação: 2016
Tipo de documento: Tese
Idioma: por
Título da fonte: Repositório Institucional da UFS
Texto Completo: https://ri.ufs.br/handle/riufs/5252
Resumo: Critical phenomena study was for many years dominated by analysis of transitions generated by thermal fluctuations. This thermal fluctuations cease at T-0, however, quantum fluctuations does not end at zero temperature. These quantum fluctuations may, under certain conditions, trigger phase transitions. In this work the Hubbard model is used to study quantum state and quantum phase transitions in strongly correlated electron systems, considering the terms of intersite hopping and Coulomb repulsion intrasite. It was developed an algorithm based on Lanczos method to solving the Hubbard model applied in different types of lattices. Analysis of algorithms efficiency were made an was observed that the standard approaches to evaluate the properties of the ground state in the Hubbard model by Lanczos method presents convergence problems when there is a significant difference between hopping parameters and Coulomb interaction. This difference is very important since the energy convergence does not necessarily reflect in a convergence of the ground state. In this work are discussed several algorithms as standard Lanczos method, the Explicit Restarted Lanczos algorithm and the Modified Explicit Restarted Lanczos algorithm. A protocol based on these algorithms using the operator S2 as s stopping criterion was developed, since through this the operator it is possible to assess the error getting from the ground state itself. The algorithm based on the ERL provides better accuracy and it is 5 times faster compared with conventional ones. The MERL-based algorithm keeps the error at the last significant digit, and its processing time is about 2.5 times longer than the ERL-based algorithm, although it is still faster than the standard Lanczos method. These analyzes pave the way for a reliable and practical evaluation of the ground-state properties not only of the Hubbard model, but also for other manybodies quantum systems. The systems analyzed were clusters of polymeric lattice AB2 tipe, one-dimensional lattice considering nears and next nears neighbors hoppings and cluster of fcc lattice. All systems showed quantum state transitions. Through the study of the spin-spin correlations of the AB2 lattices clusters it was possible to analyze in detail the behavior of these spin-spin correlation functions between sublattices of a finite system. The analysis of one-dimensional lattice with next near neighbor made it possible to use an extrapolation method, which has determined that the quantum phase transition critical point, Uc/t = 4.7, from which the system changes from a paramagnetic behavior to a ferromagnetic behavior. In the fcc lattice clusters were examined the ground state energy as a function of the particle density showed a minimum value for all the structural sizes studied. The minimum energy decreases with increasing the interaction parameter U. It was observed that the ground state energy has a minimum at n = 0.6 for U/t = W, where W denotes the non-interacting bandwidth and the face-centered cubic structure is ferromagnetic. These results, when compared to the nickel properties, shown great similarity analysis in literature, made at finite temperature and support the results of Hirsh, which proposes that the interatomic interaction exchange is dominant to driving the system to a ferromagnetic phase.
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spelling Souza, Thiago Xavier Rocha deMacêdo, Cláudio Andradehttp://lattes.cnpq.br/02084682359671382017-09-26T18:23:49Z2017-09-26T18:23:49Z2016-07-01SOUZA, Thiago Xavier Rocha de. Modelagem computacional de sistemas de elétrons fortemente correlacionados. 2016. 80 f. Tese (Pós-Graduação em Física) - Universidade Federal de Sergipe, São Cristóvão, SE, 2016.https://ri.ufs.br/handle/riufs/5252Critical phenomena study was for many years dominated by analysis of transitions generated by thermal fluctuations. This thermal fluctuations cease at T-0, however, quantum fluctuations does not end at zero temperature. These quantum fluctuations may, under certain conditions, trigger phase transitions. In this work the Hubbard model is used to study quantum state and quantum phase transitions in strongly correlated electron systems, considering the terms of intersite hopping and Coulomb repulsion intrasite. It was developed an algorithm based on Lanczos method to solving the Hubbard model applied in different types of lattices. Analysis of algorithms efficiency were made an was observed that the standard approaches to evaluate the properties of the ground state in the Hubbard model by Lanczos method presents convergence problems when there is a significant difference between hopping parameters and Coulomb interaction. This difference is very important since the energy convergence does not necessarily reflect in a convergence of the ground state. In this work are discussed several algorithms as standard Lanczos method, the Explicit Restarted Lanczos algorithm and the Modified Explicit Restarted Lanczos algorithm. A protocol based on these algorithms using the operator S2 as s stopping criterion was developed, since through this the operator it is possible to assess the error getting from the ground state itself. The algorithm based on the ERL provides better accuracy and it is 5 times faster compared with conventional ones. The MERL-based algorithm keeps the error at the last significant digit, and its processing time is about 2.5 times longer than the ERL-based algorithm, although it is still faster than the standard Lanczos method. These analyzes pave the way for a reliable and practical evaluation of the ground-state properties not only of the Hubbard model, but also for other manybodies quantum systems. The systems analyzed were clusters of polymeric lattice AB2 tipe, one-dimensional lattice considering nears and next nears neighbors hoppings and cluster of fcc lattice. All systems showed quantum state transitions. Through the study of the spin-spin correlations of the AB2 lattices clusters it was possible to analyze in detail the behavior of these spin-spin correlation functions between sublattices of a finite system. The analysis of one-dimensional lattice with next near neighbor made it possible to use an extrapolation method, which has determined that the quantum phase transition critical point, Uc/t = 4.7, from which the system changes from a paramagnetic behavior to a ferromagnetic behavior. In the fcc lattice clusters were examined the ground state energy as a function of the particle density showed a minimum value for all the structural sizes studied. The minimum energy decreases with increasing the interaction parameter U. It was observed that the ground state energy has a minimum at n = 0.6 for U/t = W, where W denotes the non-interacting bandwidth and the face-centered cubic structure is ferromagnetic. These results, when compared to the nickel properties, shown great similarity analysis in literature, made at finite temperature and support the results of Hirsh, which proposes that the interatomic interaction exchange is dominant to driving the system to a ferromagnetic phase.O estudo dos fenômenos críticos foi, por muitos anos, dominado pela análise das transições geradas por flutuações térmicas. As flutuações térmicas cessam em T-0, porém flutuações quânticas não acabam na temperatura zero. Essas flutuações de caráter quântico podem, sob certas condições, desencadear transições de fase. Neste trabalho o modelo de Hubbard é utilizado para o estudo de transições de estado quântico e de fase quântica em sistemas de elétrons fortemente correlacionados, considerando os termos de hopping intersítios e de repulsão coulombiana intrasítio. Foi desenvolvido um algoritmo com base no método de Lanczos para resolver o modelo de Hubbard aplicado a diferentes tipos de rede. Foram feitas análises da eficiência de algoritmos, nelas foi possível observar que as abordagens padrão para avaliar as propriedades do estado fundamental do modelo de Hubbard através do método de Lanczos apresentam problemas de convergência quando há uma significante diferença entre os parametros de hopping e de interação coulombiana. Esta diferença é muito relevante uma vez que a convergência da energia não reflete necessariamente em uma convergência do estado fundamental. Neste trabalho são discutidos vários algoritmos como o método de Lanczos padrão, o algoritmo Explicit Restarted Lanczos e o algoritmo Modified Explicit Restarted Lanczos. Foi desenvolvido um protocolo baseado nesses algoritmos que utiliza o valor de S2 como critério de parada do método, uma vez que através dessa grandeza é possível avaliar o erro na obtenção do estado fundamental. O algoritmo baseado no ERL proporciona uma melhor precisão é 5 vezes mais rápido quando comparado com o convencional. O algoritmo baseado no MERL mantém o erro no último dígito significativo e seu tempo de processamento é cerca de 2.5 vezes mais longo do que o algoritmo baseado no ERL, embora ainda seja mais rápido do que o método Lanczos padrão. Essas análises abrem caminho para uma avaliação confiável e prática das propriedades do estado fundamental, não só do modelo de Hubbard, mas também para muitos outros sistemas quânticos de muitos corpos. Os sistemas analisados foram clusters de rede polimérica tipo AB2, de rede unidimensional considerando hoppings tanto de primeiros quanto de segundos vizinhos e clusters de rede fcc. Todos os sistemas apresentaram transições de estado quântico. Através do estudo das correlações spin-spin do cluster da rede AB2 foi possível analisar detalhadamente o comportamento das referidas funções de correlação spin-spin entre sub-redes de um sistema finito. A análise da rede unidimensional com hopping entre segundos vizinhos possibilitou utilizar um método de extrapolação, o qual determinou que o ponto crítico de transição de fase quântica, Uc/t = 4.7, a partir do qual o sistema passa de um comportamento paramagnético para um comportamento ferromagnético. Nos clusters de rede fcc foram examinadas as energias do estado fundamental em função da densidade de partícula, observando-se a existência de um valor de mínimo de energia para todas os tamanhos estruturais estudados. Os mínimos de energia diminuem com o aumento do parâmetro de interação U. Foi observado que a energia do estado fundamental tem um mínimo em a densidade eletrônica igual a 0.6 para U/t=W, em que W denota a largura de banda não-interagente e a estrutura cúbica de face centrada mostrou-se ferromagnético. Esses resultados, quando comparados com as propriedades do níquel, mostam grande semelhança com análises na literatura feitas sob temperatura finita e suportam os resultados de Hirsh, o qual propõe que a interação interatômica de exchange é dominante na condução do sistema à uma fase ferromagnética.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal de SergipePós-Graduação em FísicaUFSBrasilFísicaFísico-químicaModelo de HubbardAlgoritmosFerromagnetismoMétodo do LanczosFase quânticaExplicit Restarted LanczosModified Explicit Restarted LanczosCIENCIAS EXATAS E DA TERRA::FISICAModelagem computacional de sistemas de elétrons fortemente correlacionadosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSORIGINALTHIAGO_XAVIER_ROCHA_SOUZA.pdfapplication/pdf822461https://ri.ufs.br/jspui/bitstream/riufs/5252/1/THIAGO_XAVIER_ROCHA_SOUZA.pdf5beb15f2ab175952da6b338f9878373eMD51TEXTTHIAGO_XAVIER_ROCHA_SOUZA.pdf.txtTHIAGO_XAVIER_ROCHA_SOUZA.pdf.txtExtracted texttext/plain133775https://ri.ufs.br/jspui/bitstream/riufs/5252/2/THIAGO_XAVIER_ROCHA_SOUZA.pdf.txta334306b1ec046910c939167e1c9370fMD52THUMBNAILTHIAGO_XAVIER_ROCHA_SOUZA.pdf.jpgTHIAGO_XAVIER_ROCHA_SOUZA.pdf.jpgGenerated Thumbnailimage/jpeg1234https://ri.ufs.br/jspui/bitstream/riufs/5252/3/THIAGO_XAVIER_ROCHA_SOUZA.pdf.jpgdc5c6341cf81fb98c29d1cc95f6c3879MD53riufs/52522018-06-13 20:10:11.121oai:ufs.br:riufs/5252Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2018-06-13T23:10:11Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.por.fl_str_mv Modelagem computacional de sistemas de elétrons fortemente correlacionados
title Modelagem computacional de sistemas de elétrons fortemente correlacionados
spellingShingle Modelagem computacional de sistemas de elétrons fortemente correlacionados
Souza, Thiago Xavier Rocha de
Física
Físico-química
Modelo de Hubbard
Algoritmos
Ferromagnetismo
Método do Lanczos
Fase quântica
Explicit Restarted Lanczos
Modified Explicit Restarted Lanczos
CIENCIAS EXATAS E DA TERRA::FISICA
title_short Modelagem computacional de sistemas de elétrons fortemente correlacionados
title_full Modelagem computacional de sistemas de elétrons fortemente correlacionados
title_fullStr Modelagem computacional de sistemas de elétrons fortemente correlacionados
title_full_unstemmed Modelagem computacional de sistemas de elétrons fortemente correlacionados
title_sort Modelagem computacional de sistemas de elétrons fortemente correlacionados
author Souza, Thiago Xavier Rocha de
author_facet Souza, Thiago Xavier Rocha de
author_role author
dc.contributor.author.fl_str_mv Souza, Thiago Xavier Rocha de
dc.contributor.advisor1.fl_str_mv Macêdo, Cláudio Andrade
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/0208468235967138
contributor_str_mv Macêdo, Cláudio Andrade
dc.subject.por.fl_str_mv Física
Físico-química
Modelo de Hubbard
Algoritmos
Ferromagnetismo
Método do Lanczos
Fase quântica
topic Física
Físico-química
Modelo de Hubbard
Algoritmos
Ferromagnetismo
Método do Lanczos
Fase quântica
Explicit Restarted Lanczos
Modified Explicit Restarted Lanczos
CIENCIAS EXATAS E DA TERRA::FISICA
dc.subject.eng.fl_str_mv Explicit Restarted Lanczos
Modified Explicit Restarted Lanczos
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::FISICA
description Critical phenomena study was for many years dominated by analysis of transitions generated by thermal fluctuations. This thermal fluctuations cease at T-0, however, quantum fluctuations does not end at zero temperature. These quantum fluctuations may, under certain conditions, trigger phase transitions. In this work the Hubbard model is used to study quantum state and quantum phase transitions in strongly correlated electron systems, considering the terms of intersite hopping and Coulomb repulsion intrasite. It was developed an algorithm based on Lanczos method to solving the Hubbard model applied in different types of lattices. Analysis of algorithms efficiency were made an was observed that the standard approaches to evaluate the properties of the ground state in the Hubbard model by Lanczos method presents convergence problems when there is a significant difference between hopping parameters and Coulomb interaction. This difference is very important since the energy convergence does not necessarily reflect in a convergence of the ground state. In this work are discussed several algorithms as standard Lanczos method, the Explicit Restarted Lanczos algorithm and the Modified Explicit Restarted Lanczos algorithm. A protocol based on these algorithms using the operator S2 as s stopping criterion was developed, since through this the operator it is possible to assess the error getting from the ground state itself. The algorithm based on the ERL provides better accuracy and it is 5 times faster compared with conventional ones. The MERL-based algorithm keeps the error at the last significant digit, and its processing time is about 2.5 times longer than the ERL-based algorithm, although it is still faster than the standard Lanczos method. These analyzes pave the way for a reliable and practical evaluation of the ground-state properties not only of the Hubbard model, but also for other manybodies quantum systems. The systems analyzed were clusters of polymeric lattice AB2 tipe, one-dimensional lattice considering nears and next nears neighbors hoppings and cluster of fcc lattice. All systems showed quantum state transitions. Through the study of the spin-spin correlations of the AB2 lattices clusters it was possible to analyze in detail the behavior of these spin-spin correlation functions between sublattices of a finite system. The analysis of one-dimensional lattice with next near neighbor made it possible to use an extrapolation method, which has determined that the quantum phase transition critical point, Uc/t = 4.7, from which the system changes from a paramagnetic behavior to a ferromagnetic behavior. In the fcc lattice clusters were examined the ground state energy as a function of the particle density showed a minimum value for all the structural sizes studied. The minimum energy decreases with increasing the interaction parameter U. It was observed that the ground state energy has a minimum at n = 0.6 for U/t = W, where W denotes the non-interacting bandwidth and the face-centered cubic structure is ferromagnetic. These results, when compared to the nickel properties, shown great similarity analysis in literature, made at finite temperature and support the results of Hirsh, which proposes that the interatomic interaction exchange is dominant to driving the system to a ferromagnetic phase.
publishDate 2016
dc.date.issued.fl_str_mv 2016-07-01
dc.date.accessioned.fl_str_mv 2017-09-26T18:23:49Z
dc.date.available.fl_str_mv 2017-09-26T18:23:49Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.citation.fl_str_mv SOUZA, Thiago Xavier Rocha de. Modelagem computacional de sistemas de elétrons fortemente correlacionados. 2016. 80 f. Tese (Pós-Graduação em Física) - Universidade Federal de Sergipe, São Cristóvão, SE, 2016.
dc.identifier.uri.fl_str_mv https://ri.ufs.br/handle/riufs/5252
identifier_str_mv SOUZA, Thiago Xavier Rocha de. Modelagem computacional de sistemas de elétrons fortemente correlacionados. 2016. 80 f. Tese (Pós-Graduação em Física) - Universidade Federal de Sergipe, São Cristóvão, SE, 2016.
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