Chapter

Dynamical Mean-field Theories of Correlation and Disorder

E. Miranda and V. Dobrosavljević

in Conductor-Insulator Quantum Phase Transitions

Published in print June 2012 | ISBN: 9780199592593
Published online September 2012 | e-ISBN: 9780191741050 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199592593.003.0006
Dynamical Mean-field Theories of Correlation and Disorder

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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

Chapter.  37421 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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