TAILIEUCHUNG - Constructing electronic phase diagram for the half-filled hubbard model with disorder

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. | Communications in Physics, Vol. 28, No. 2 (2018), pp. 163-168 DOI: CONSTRUCTING ELECTRONIC PHASE DIAGRAM FOR THE HALF-FILLED HUBBARD MODEL WITH DISORDER HOANG ANH TUAN † AND NGUYEN THI HAI YEN Institute of Physics, Vietnam Academy of Science and Technology † E-mail: hatuan@ Received 7 March 2018 Accepted for publication 15 April 2018 Published 16 June 2018 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. Keywords: phase diagram, disordered Hubbard model, Anderson insulator . Classification numbers: . I. INTRODUCTION The development of the quantum theory of solids led to the detection of different mechanisms being able to cause a metal - insulator transition (MIT). The correlation induced metal insulator transitions are called Mott transition. An important model to study electron correlations and Mott transition is the famous Hubbard model (HM). On the other hand, disorder in solids, such as impurities or vacancies, was found to strongly modify band theory predictions. In 1958, Anderson showed in his analysis of a disordered tight binding model that a sufficient amount of disorder hinders the diffusion of particles [1]. Coherent backscattering processes cause a localization of the particle. In particular, the localization of states at the Fermi level induces a metal insulator transition, the Anderson transition. The interplay of disorder and interactions leads to many important and unexpected effects. Among them, the MIT at non-integer filling, have been found by Byczuk and coworkers by .

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