O método do grupo de renormalização de teoria de campos aplicado ao modelo de Anderson de uma impureza
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Data
2012-06-21
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Universidade Federal de Goiás
Resumo
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.
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Citação
ROCHA, Francisco Manoel Bezerra e. O método do grupo de renormalização de teoria de campos aplicado ao modelo de Anderson de uma impureza. 2012. 75 f. Dissertação (Dissertação em Física) - Universidade Federal de Goiás, Goiânia, 2012.