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We generalize the typical medium dynamical cluster approximation (TMDCA) and the local Blackman, Esterling, and Berk (BEB) method for systems with off-diagonal disorder. Using our extended formalism we perform a systematic study of the effects of non-local disorder-induced correlations and of off-diagonal disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three-dimensional Anderson model with configuration dependent hopping and find fast convergence with modest cluster sizes. Our results are in good agreement with the data obtained using exact diagonalization, and the transfer matrix and kernel polynomial methods.
We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in the low a
By merging single-site typical medium theory with density functional theory we introduce a self-consistent framework for electronic structure calculations of materials with substitutional disorder which takes into account Anderson localization. The s
We report the development and application of a new method for carrying out computational investigations of the effects of mass and force-constant (FC) disorder on phonon spectra. The method is based on the recently developed typical medium dynamical
We describe non-conventional localization of the midband E=0 state in square and cubic finite bipartite lattices with off-diagonal disorder by solving numerically the linear equations for the corresponding amplitudes. This state is shown to display m
We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr{e} model and investigate its phase diagram by using the symmetry and the multifractal analysis. It was shown in a recent work ({it Phys. Rev. B} {bf 93}, 205441