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Bulletin of the American Physical Society

Local Analysis of Disorder Driven Insulator-to-Metal Transition in the 2D Mott-Hubbard Model

Joseph C. Szabo, Kyungmin Lee, Nandini Trivedi, Jared O’Neal

Published Mar 7, 2019• 0 citations
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Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
The statistical dynamical mean field theory is used to study the metal-insulator transition in the two-dimensional Falicov-Kimball model with local disorder. Within the theory, the local density of states and its distributions are calculated. As a measure of the metal-insulator transition driven by correlation and disorder, the most probable value of the local density of states is determined. The most probable value of the local density of states is found to exhibit a discontinuity when the system crosses from extended states to localization. A phase diagram is also presented.