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Conductor-Insulator Quantum Phase Transitions$
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Vladimir Dobrosavljevic, Nandini Trivedi, and James M. Valles, Jr.

Print publication date: 2012

Print ISBN-13: 9780199592593

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199592593.001.0001

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Dynamical Mean-field Theories of Correlation and Disorder

Dynamical Mean-field Theories of Correlation and Disorder

Chapter:
(p.161) 6 Dynamical Mean-field Theories of Correlation and Disorder
Source:
Conductor-Insulator Quantum Phase Transitions
Author(s):

E. Miranda

V. Dobrosavljević

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199592593.003.0006

This chapter provides a review of recently-developed Dynamical Mean-Field Theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. The chapter first describes the standard DMFT approach, which is exact in the limit of large coordination, and explain why in its simplest form it cannot capture either Anderson localization or the glassy behavior of electrons. Various extensions of DMFT are then described, including statistical DMFT, typical medium theory, and extended DMFT, methods specifically designed to overcome the limitations of the original formulation. The chapter provides an overview of the results obtained using these approaches, including the formation of electronic Griffiths phases, the self-organized criticality of the Coulomb glass, and the two-fluid behavior near Mott-Anderson transitions. Finally, the chapter outlines research directions that may provide a route to bridge the gap between the DMFT-based theories and the complementary diffusion-mode approaches to the metal-insulator

Keywords:   Dynamical Mean-Field Theory, strong electronic correlations, statistical DMFT, typical medium theory, EDMDT, sigma model, diffusion modes, electronic Griffiths phases, disorder-driven non-Fermi liquid behavior

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