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arXiv:0902.0296 · NATO science for peace and security series. B, Physics and biophysics

Local Moment Approach to Multi-Orbital Anderson and Hubbard Models

Anna Kauch, Krzysztof Byczuk

Published Jan 1, 2008• 1 citation
arXivHTMLPDF
DOI
10.1007/978-1-4020-8512-3_7

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The local moment approach (LMA) of Logan et al. and its modification is summarized here. The existence of the local moments is taken from the outset and their values are determined through variational principle by minimizing the corresponding ground state energy. The LMA is used to solved a multi-orbital single impurity Anderson model. The method is also applied to solve the dynamical mean-field equations for the multi-orbital Hubbard model. In particular, the Mott-Hubbard metal–insulator transition is addressed within this approach.
Anderson localization is a quantum phenomenon in which disorder localizes electronic wave functions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the standard transfer matrix method, we extract the localization length from the modular density matrix in quasi-one-dimensional systems. This approach successfully captures the metal-insulator transition in the three-dimensional Anderson model and in the two-dimensional Anderson model with spin-orbit coupling. It can be also readily extended to multi-orbital systems. We further generalize the formalism to interacting systems, showing that the one-dimensional spinless attractive model exhibits the expected metallic phase, consistent with previous studies. More importantly, we demonstrate the existence of a two-dimensional metallic tendency in the presence of Hubbard interactions and disorder. This method offers a new perspective on Anderson localization and its interplay with interactions.