Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice

In this work, we analyze the single-particle Green function of the Hubbard model on the Bethe lattice with an infinite number of nearest neighbors at zero temperature. The Hubbard model is conceptually the simplest many-electron model. Nevertheless, it poses a most difficult many-body problem. Exce...

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Bibliographic Details
Main Author: Ruhl, Daniel F.
Contributors: Gebhard, Florian (Prof. Dr.) (Thesis advisor)
Format: Dissertation
Language:English
Published: Philipps-Universität Marburg 2010
Physik
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Summary:In this work, we analyze the single-particle Green function of the Hubbard model on the Bethe lattice with an infinite number of nearest neighbors at zero temperature. The Hubbard model is conceptually the simplest many-electron model. Nevertheless, it poses a most difficult many-body problem. Except in one spatial dimension, no exact solution has been found up to today. Therefore, systematic analytical approximations are of major importance as they provide results in the thermodynamic limit against which numerical methods can be tested. We aim to calculate the single-particle density of states and the gap for charge-carrying single-particle excitations. Both of these quantities are rather difficult to obtain in numerical studies which necessarily deal with rather small system sizes. Reliable analytical results provide reliable benchmark tests for the numerics. We employ the Dynamical Mean-Field theory (DMFT), which permits the mapping of the Hubbard model in infinite dimensions or, equivalently, with an infinite number of nearest neighbors, onto an effective quantum impurity system. We use the Single Impurity Anderson Model (SIAM) as the quantum impurity model. New to our approach is the fact that we solve the DMFT equations for the Mott-Hubbard insulator up to third order in 1/U . We achieve this goal with the help of the Kato-Takahashi perturbation after successfully adapting it to our problem. This is the first time an analytical solution of the DMFT self-consistency equations for the insulator has been found.
DOI:https://doi.org/10.17192/z2010.0377