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Communications in Physics

Constructing Electronic Phase Diagram for the Half-filled Hubbard Model with Disorder

Hoàng Anh Tuấn, Nguyen Thi Hai Yen

Published Jul 17, 2018• 2 citations
Publisher

Abstract

The electronic phase diagram of strongly correlated systems with disorder is constructed using the typical-medium theory. For half-filled system, the combination of the linearized dynamical mean field theory and equation of motion approach allows to derive the explicit equations determining the boundary between the correlated metal, Mott insulator, and Anderson insulator phases. Our phase diagram is consistent with those obtained by the more sophisticated methods.

DOI
10.15625/0868-3166/28/2/11673

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The electronic phase diagram of strongly correlated systems with disorder is constructed using the typical-medium theory. For half-filled system, the combination of the linearized dynamical mean field theory and equation of motion approach allows to derive the explicit equations determining the boundary between the correlated metal, Mott insulator, and Anderson insulator phases. Our phase diagram is consistent with those obtained by the more sophisticated methods.
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Abstract We study metal-insulator phase diagram in the half-filled disordered Hubbard model at finite temperature. We calculate the averaged local density of states at the Fermi level and the site occupation as a function of the on-site energy at finite temperature by using typical medium theory with an impurity solver of equation of motion method. Although the metallicity in the correlated metallic region changes with temperature change, the phase diagram is almost temperature independent. We find fairly good agreement between our site occupation and those obtained by the typical medium method with other impurity solver.
Abstract We study the half-filled Hubbard model with Anderson and Coulomb disorder by mean of dynamical mean field theory using the geometrically averaged local density of states. The paramagnetic phase diagram of the model as a function of the Coulomb interaction and Anderson disorder strength is obtained. The spectral phase diagrams of the ground states for the model are also constructed and discussed. We show that in the intermediate and strong interaction regimes, the Coulomb disorder leads the metallic and Mott insulator phase regions shrink, while the Anderson insulator region is enlarged.
We investigate the effects of Coulomb disorder on the half-filled ionic Hubbard model within the framework of dynamical mean-field theory (DMFT), using the equation-of-motion method as the impurity solver, combined with typical medium theory (TMT). In contrast to conventional disordered Hubbard models, the ionic Hubbard model contains a staggered ionic potential that introduces additional competition between band-insulating and correlation-driven insulating tendencies. We analyze how this ionic potential modifies the electronic phases induced by Coulomb disorder through the arithmetic and geometric averages of the local density of states. In the absence of disorder, the system exhibits metallic (M), Mott-insulating (MI), and band-insulating (BI) phases. When Coulomb disorder is introduced, Anderson-insulating (AI) behavior and localized states (LS) inside the Mott gap are also observed. In particular, the LS regime appears between the metallic and Mott-insulating phases at small ionic potentials, whereas the AI regime develops for sufficiently large values of the Coulomb interaction and ionic potential. Our results show that the interplay between ionic potential, electron correlation, and disorder substantially influences the localization behavior and insulating characteristics of the ionic Hubbard model.
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.