Anderson localization vs. Mott-Hubbard metal-insulator transition in disordered, interacting lattice fermion systems

Abstract

We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the Dynamical Mean-Field Theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground-state phase diagram of the Anderson-Hubbard model at half filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.

25 pages, 5 figures, typos corrected, references updated

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• Interacting fermions in 1D disordered lattices: Exploring localization and transport properties with lattice density-functional theories
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• Anderson-Mott transition in a disordered Hubbard model with correlated hopping
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• Realization of a "Two Relaxation Rates" in the Hubbard-Falicov-Kimball Model
• Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion
• Hidden Anderson Localization in Disorder-Free Ising-Kondo Lattice
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