Dynamical mean-field theories of correlation and disorder

Abstract

We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe 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. We provide 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, we outline 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 transition.

78 pages, 19 figures; To be published in "Conductor Insulator Quantum Phase Transitions", edited by V. Dobrosavljevic, N. Trivedi, and J.M. Valles Jr., Oxford University Press, 2013, ISBN 9780199592593

References in corpus (3)

• Spatial inhomogeneity and strong correlation physics: a dynamical mean field study of a model Mott-insulator/band-insulator heterostructure
• Effects of dissipation on a quantum critical point with disorder
• Theory of smeared quantum phase transitions

Cited by in corpus (5)

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• Dynamical mean-field theory of the Anderson-Hubbard model with local and non-local disorder in tensor formulation
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Thermodynamic properties of correlated fermions in lattices with spin-dependent disorder
• Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems