The Hubbard Model with Local Disorder in d = ∞
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The scattering of electrons caused by their mutual interaction and by the presence of static disorder, respectively, can lead to very different, and even opposite, effects. For example, on a cubic lattice at half-filling an arbitrarily weak repulsive Hubbard interaction between electrons is sufficient to induce antiferromagnetic long-range order (AFLRO). By contrast, the presence of randomness opposes long-range spatial order. The simultaneous presence of disorder and interactions in electronic systems can hence be expected to lead to fundamentally new phenomena which have no analog in interacting, non-random and non-interacting, disordered systems, respectively , To obtain a global picture of the properties of such systems it is desirable to know the solution of a simple, microscopic model which is valid for all input parameters (interaction, disorder, temperature, band filling). Since exact solutions are not available in d = 2, 3 one would like to construct, at least, a thermodynamically consistent mean-field theory that is valid also at strong coupling. Such a (non-perturbative) approximation is provided by the exact solution of a model in d = ∞. It is now known that even in the limit d → ∞ [2,3] the Hubbard interaction remains dynamical  and leads to a highly non-trivial single-site problem [5–8] with infinitely many coupled quantum degrees of freedom. This problem is, in fact, equivalent with an Anderson impurity model complemented by a self-consistency condition  and is thus amenable to numerical investigations  within a finite-temperature quantum Monte-Carlo approach . In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,10] the Mott-Hubbard transition [11–13, 10], transport properties  and lately also superconductivity in a two-band version  of the Hubbard model in d = ∞.
KeywordsHubbard Model Random Potential Antiferromagnetic Phase Magnetic Phase Diagram Band Filling
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