Dynamical mean field study of the two-dimensional disordered Hubbard model

Abstract

We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean-field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration-averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarterand half-filling and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.

Self-consistent study of Anderson localization in the Anderson-Hubbard model in two and three dimensions

“…2, this provides even in d = 2 an excellent quantitative estimate for the results of the self-consistent theory not only for large disorder, as expected, but also for intermediate disorder. The nonmonotonic behavior is reproduced by numerical methods for finite-size systems, i.e., by quantum Monte Carlo (QMC) simulations 4,7 and statistical dynamical mean field theory (DMFT), 8 with the maximum of ξ(U ) occurring almost precisely at U (1D) ξ . In the case of the QMC results 7 the nonmonotonicity can be inferred from the dependence of the finite-temperature conductivity on U .…”

“…In Ref. [8] the on-site energies were calculated as poles of the atomic limit Green's function of the Anderson-Hubbard Hamiltonian, resulting in precisely the same Hamiltonian as our effective model [Eqs. (2) and (3)].…”

“…Recent numerical works showed that the presence of interactions can at least suppress significantly the localizing effect of the disorder. [4][5][6][7][8][9]15 One of the ideas proposed to explain the delocalizing effect is screening of the random potential by the interaction, discussed controversially in the literature. A detailed analysis of this screening effect is the subject of this paper.…”

Localization of correlated fermions in optical lattices with speckle disorder

“…For this reason we also investigate fermions on a square lattice within RDMFT. 26,27,34,35 Besides describing the Mott-Hubbard metal-insulator transition and magnetic order, RDMFT is also capable of treating spatial inhomogeneities such as disorder. As in DMFT, each lattice site is mapped onto a single-impurity Anderson Hamiltonian within RDMFT, where the hybridization function has to be determined self-consistently.…”

“…For this purpose, we employ the statistical dynamical mean-field theory (DMFT) 8,[26][27][28] to solve the Anderson-Hubbard Hamiltonian numerically. The statistical DMFT incorporates both strong correlations and disorder-induced fluctuations and is known to give accurate results for highdimensional systems, i.e.…”