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arXiv:0810.2958 · Physical Review Letters

Competition between Anderson Localization and Antiferromagnetism in Correlated Lattice Fermion Systems with Disorder

Krzysztof Byczuk, Walter Hofstetter, D. Vollhardt

Published Apr 7, 2009• 62 citations
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Abstract

The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.

DOI
10.1103/physrevlett.102.146403

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The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.
The interplay between disorder acting only on particles with a given spin projection (spin-dependent disorder) and antiferromagnetic long-range order is explored. To this end the magnetic ground state phase diagram of the Hubbard model at half-filling is computed within dynamical mean-field theory combined with the geometric average over disorder, a method sensitive to Anderson localization. Four distinct phases are identified: a paramagnetic metal, an antiferromagnetic insulator, and two types of spin-selective localized phases. The phase diagram may be tested experimentally using cold fermions in optical lattices subject to spin-dependent random potentials.
The magnetic phases induced by the interplay between disorder acting only on particles with a given spin projection ("spin-dependent disorder") and a local repulsive interaction is explored. To this end the magnetic ground state phase diagram of the Hubbard model at half-filling is computed within dynamical mean-field theory combined with the geometric average over disorder, which is able to describe Anderson localization. Five distinct phases are identified: a ferromagnetically polarized metal, two types of insulators, and two types of spin-selective localized phases. The latter four phases possess different long-range order of the spins. The predicted phase diagram may be tested experimentally using cold fermions in optical lattices subject to spin-dependent random potentials.
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.
The magnetic phases induced by the interplay between disorder acting only on particles with a given spin projection ('spin-dependent disorder') and a local repulsive interaction is explored. To this end the magnetic ground state phase diagram of the Hubbard model at half-filling is computed within dynamical mean-field theory combined with the geometric average over disorder, which is able to describe Anderson localization. Five distinct phases are identified: a ferromagnetically polarized metal, two types of insulators, and two types of spin-selective localized phases. The latter four phases possess different long-range order of the spins. The predicted phase diagram may be tested experimentally using cold fermions in optical lattices subject to spin-dependent random potentials.
Strongly correlated fermions in a crystal or in an optical lattice in the presence of binary-alloy disorder are investigated. We employ the statistical dynamical mean-field theory, which incorporates both fluctuations due to disorder and local correlations due to interaction, to solve the Anderson-Hubbard model. Localization due to disorder is studied by means of the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram consisting of disordered correlated metal, Anderson-Mott insulator, and band insulator.
The interplay between local, repulsive interactions and disorder acting only on one spin orientation of lattice fermions (``spin-dependent disorder'') is investigated. The nonmagnetic disorder vs interaction phase diagram is computed using dynamical mean-field theory in combination with the geometric average over disorder. The latter determines the typical local density of states and is therefore sensitive to Anderson localization. The effect of spin-dependent disorder is found to be very different from that of conventional disorder. In particular, it destabilizes the metallic solution and leads to a spin-selective, localized phase at weak interactions and strong disorder.