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Doctoral Thesis
DOI
10.11606/T.76.1994.tde-07052014-143759
Document
Author
Full name
Jeremias Borges da Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1994
Supervisor
Committee
Oliveira, Luiz Nunes de (President)
Caldeira, Amir Ordacgi
Fóglio, Mário Eusébio
Monaco, Roberto e Lagos
Troper, Amós
Title in Portuguese
Novo método de grupo de renormalização numérico aplicado ao cálculo da susceptibilidade magnética no modelo de Anderson de duas impurezas
Keywords in Portuguese
Acoplamento forte
Efeito Kondo
Impurezas magnéticas
Abstract in Portuguese
Este trabalho introduz uma nova discretização da banda de condução no método de Grupo de Renormalização Numérico. Com essa técnica, a susceptibilidade magnética do modelo de Anderson de duas impurezas, no limite Kondo, e calculada. Como ilustração, a densidade espectral do modelo também é calculada. A nova técnica baseia-se na simetria de paridade do modelo para discretizar diferentemente à banda de condução associada a cada paridade. Sua extensão ao modelo de rede é indicada. A técnica reduz o tempo computacional e permite usar maiores valores do parâmetro de discretização do que no método tradicional. Para um mesmo tempo de cálculo, nossos resultados são muito mais precisos do que os encontrados na literatura. A susceptibilidade é calculada na aproximação de acoplamento independente da energia. Uma interação de troca, tipo RKKY, é somado ao Hamiltoniano do modelo. Para acoplamento ferromagnético, obtém-se efeito Kondo de dois estágios. O estado fundamental é singleto com defasagem de PI/2 na banda de condução. Para acoplamento antiferromagnético fraco, um efeito Kondo é obtido. Para fortes acoplamentos antiferromagnéticos, o estado fundamental e singleto sem defasagens. Um ponto fixo instável é observado separando as regiões de estado fundamental Kondo e antiferromagnético. Nesse ponto a susceptibilidade é nula e a defasagem é indefinida.
Title in English
New method of numerical renormalization group applied to the calculation of the magnetic susceptibility in the two-impurity
Keywords in English
Kondo effect
Magnetic impurities
Strong coupling
Abstract in English
This work introduces an extension of the Numerical Renormalization Group approach to compute thermodynamically properties of impurities in metals, based on a novel logarithmic discretization of the conduction band. On the basis of the new method, the thermal dependence of the magnetic susceptibility for the Kondo limit of the two-impurity Anderson model is computed. As another illustration, the impurity spectral density for the same model is calculated analytically in the weakly correlated regime. The new approach takes advantage of the parity-inversion symmetry of the model to discretize differently the odd and the even conduction channels (for Ni impurities, the conduction band could likewise be divided into Ni channels, each of which would be discretized in a different way). The resulting mesh describes better the continuum of the conduction states than the mesh in the standard Numerical Renormalization Group method; as a consequence, the new procedure is substantially less expensive when computing any given thermodynamical property with a given accuracy, thus we are able to compute the temperature dependence of the magnetic susceptibility with a small fraction of the effort involved in the recently reported computation of the ground state properties for the two impurity Kondo model. As in previous Renormalization Group work, the model Hamiltonian is diagonalized within the energy-independent coupling approximation. One well-known shortcoming of this approximation is its inability to generate antiferromagnetic RKKY couplings between the impurities; to compensate, again following previous work; we have added to the Hamiltonian an artificial exchange coupling Io. For weak antiferromagnetic or ferromagnetic couplings, the effective magnetic moment of the impurities decreases with temperature, and as in the one-impurity Kondo effect, the ground-state conduction band is phase shifted by PI /2. For strong ferromagnetic coupling, the Kondo effect takes place in two stages, one for each conduction channel. For strong antiferromagnetic coupling, the magnetic moment also decreases, rapidly, with temperature, but the ground state conduction-band phase shift is zero. The regions of zero and PI /2 ground-state phase shifts are separated by an unstable fixed point. At this point, the magnetic susceptibility vanishes.
 
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Publishing Date
2014-05-08
 
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