Finite-cluster typical medium theory for disordered electronic systems

Abstract

We use the recently developed typical medium dynamical cluster (TMDCA) approach [Ekuma et al., Phys. Rev. B 89, 081107 (2014)] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three dimensions, we demonstrate the importance of both spatial correlations and a typical environment for the proper characterization of the localization transition in all the disorder distributions studied. As a function of increasing cluster size, the TMDCA systematically recovers the re-entrance behavior of the mobility edge for disorder distributions with finite variance, obtaining the correct critical disorder strengths, and shows that the order parameter critical exponent for the Anderson localization transition is universal. The TMDCA is computationally efficient, requiring only a small cluster to obtain qualitative and quantitative data in good agreement with numerical exact results at a fraction of the computational cost. Our results demonstrate that the TMDCA provides a consistent and systematic description of the Anderson localization transition.

Competition between disorder and Coulomb interaction in a two-dimensional plaquette Hubbard model

“…We employ a continuous-time quantum Monte Carlo algorithm as the DMFT impurity solver 33,34 in our own implementation 35 . Disorder effects are evaluated with the coherent potential approximation 16,36 .…”

Study of multiband disordered systems using the typical medium dynamical cluster approximation

“…Since the two bands are degenerate and the disorder strength for each band is also identical, the calculated average DOS will be the same for each band, so we only plot the quantities for one of the bands in the following results, as it is enough to characterize the properties of the system. In our formalism, in order to disorder average instead of performing the very expensive enumeration of all disorder configurations, which scales as 2 2Nc , we perform a stochastic sampling of configurations which greatly reduces the computational cost 25 . This is so we can study larger systems.…”

Melting and crystallization in large sized copper cluster

“…Cluster is considered as a transition state from molecular to bulk materials. The properties of these nanoclusters are qualitatively different from the ones of their constituent parts (being either atoms or molecules) and from those of macroscopic pieces of matters [4][5][6][7][8]. Therefore, it is of fundamental interest to understand how their properties depend on size, and in particular on the bulk-like limit.…”