O método do grupo de renormalização de teoria de campos aplicado ao modelo de Anderson de uma impureza

• Ano de defesa: 2012
• Autor(a) principal: Rocha, Francisco Manoel Bezerra e
• Orientador(a): Silva, Hermann Freire Ferreira Lima e
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Fisica (IF)
• Departamento: Instituto de Física - IF (RG)
• País: Brasil
• Palavras-chave em Português: Grupo de renormalização de teoria de campos; Modelo de Anderson; Single impurity Anderson model
• Palavras-chave em Inglês: Renomarlization group method of field theory
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tde/2906

We apply the perturbative eld-theoretical renormalization group (RG) implemented within an approach which considers the calculation for the e ective couplings up to one loop and the computation of the self-energy up to two loops of the single-impurity Anderson model with particle-hole symmetry. To this end, we follow Feynman's diagrammatic method applied to the model and we begin our analysis by calculating the so-called vertex corrections up to one loop. The e ect of correlations on the single-particle excitations is viewed most clearly by means of the computation of the self-energy and its closely-related quantity: the quasiparticle weight. Moreover, to determine the nature of the ground state of the model, we also perform the RG calculation of the so-called uniform spin susceptibility. Then we apply the RG technique, adapting it conveniently to our problem at hand. The next step consists of deriving analytically and solving numerically the coupled di erential RG ow equations for the e ective couplings, the quasiparticle weight and the uniform spin susceptibility. We show that our results agree qualitatively with other analytical works available in the literature, such as, e.g., the functional RG. To benchmark our method, we compare our results with Wilson's numerical RG data. This latter method provides highly accurate numerical results for the quantities analyzed here and, for this reason, it will be an important check for our analytical method. Since the eldtheoretical RG turns out to be a exible technique and also simpler to be implemented at higher orders if compared to some versions of the functional RG method, we argue here that the present methodology could potentially o er a possible alternative to other analytic RG methods to describe eletronic correlations within the single-impurity Anderson model.