Mott-Hubbard and Anderson metal-insulator transitions in correlated lattice fermions with binary disorder

Abstract

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 AndersonHubbard 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.

Localization of correlated fermions in optical lattices with speckle disorder

“…52 For further details, the reader is referred to the work by M. Potthoff et al 52 and our earlier work. 28 …”

“…28,49 This procedure is motivated by the fact that the extended states are given by a branch cut on the real axis of the single-particle Green's function, whereas the localized states are characterized by a dense distribution of poles in the thermodynamic limit. 56 Let us consider a single particle initially located at site 0 on a finite lattice and let |ψ n denote the complete set of single particle energy eigenstates on the lattice with eigenenergies E n .…”

“…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.…”

Correlated electrons in the presence of disorder

“…Calculating the full probability distribution of the LDOS typically requires the inclusion of a large number of impurity sites, which for interacting systems is hard to achieve computationally, although there have been recent successful attempts in this direction [50]. A more efficient approach is based on identifying a generalized average which yields the best approximation to the typical value.…”

Disorder-induced zero-bias anomaly in the Anderson-Hubbard model: Numerical and analytical calculations

“…Furthermore, the evidence for a soft gap in exact diagonalization calculations is less well established, 27 and it is possible that quantum fluctuations fill in the soft gap. Another common approximation, dynamical mean field theory (DMFT), 12,15,18,[29][30][31][32][33] includes strong correlation physics, but has not found a ZBA at all. It has been argued 34 that this is because of nonlocal contributions to the self-energy neglected in these calculations.…”