Controlled mean-field theory for disordered electronic systems: Single-particle properties

Vlaming, R.; Vollhardt, D.

doi:10.1103/physrevb.45.4637

Cited by 93 publications

(90 citation statements)

References 33 publications

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“…If in the DMFT the effect of local disorder is taken into account through the arithmetic mean of the LDOS one obtains, in the absence of interactions (U = 0), the coherent potential approximation (CPA) [30,118], which does not describe the physics of Anderson localization. To overcome this deficiency Dobrosavljević and collaborators formulated a variant of the DMFT where the geometrically averaged LDOS is computed from the solutions of the selfconsistent stochastic DMFT equations [119] which is then incorporated into the self-consistency cycle [120].…”

Section: Electronic Correlations and Disordermentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

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Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter. Motivation Electronic CorrelationsAlready in 1937, at the outset of modern solid state physics, de Boer and Verwey [1] drew attention to the surprising properties of materials with incompletely filled 3d-bands. This observation prompted Mott and Peierls [2] to discuss the interaction between the electrons. Ever since transition metal oxides (TMOs) were investigated intensively [3]. It is now well-known that in many materials with partially filled electron shells, such as the 3d transition metals V and Ni and their oxides, or 4f rare-earth metals such as Ce, electrons occupy narrow orbitals. The spatial confinement enhances the effect of the Coulomb interaction between the electrons, making them "strongly correlated". Correlation effects can lead to profound quantitative and qualitative changes of the physical properties of electronic systems as compared to non-interacting particles. In particular, they often respond very strongly to changes in external parameters. This is expressed by large renormalizations of the response functions of the system, e.g., of the spin susceptibility and the charge compressibility. In particular, the interplay between the spin, charge and orbital degrees of freedom of the correlated d and f electrons and with the lattice degrees of freedom leads to an amazing multitude of ordering phenomena and other fascinating properties, including high temperature superconductivity, colossal magnetoresistance and Mott metal-insulator transitions [3].arXiv:1109.4833v1 [cond-mat.str-el]

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Section: Electronic Correlations and Disordermentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

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“…Studying correlated and disordered lattice fermions within statistical DMFT, we found that it is useful to compare the resulting spectral functions to those determined within the CPA. 25,54,55 Within CPA the hybridization Γ(ω) is given by…”

Section: B Interacting Systemsmentioning

confidence: 99%

“…[21][22][23] This mean-field theory is fully non-perturbative and in combination with density functional theory it is capable of describing properties of real solid-state systems. 24 An extension of DMFT, which includes disorder effects, was performed both, in analogy to the well-known coherent potential approximation (CPA), 25,26 and within a fully stochastic approach to incorporate effects of Anderson localization. 27,28 Since the latter approach is computationally very expensive if one treats correlation effects on a rigorous level and keeps sufficiently large ensembles of disorder realizations, the typical medium theory (TMT-) DMFT was developed.…”

Section: Introductionmentioning

confidence: 99%

Mott-Hubbard and Anderson metal-insulator transitions in correlated lattice fermions with binary disorder

2010

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Strongly correlated fermions in a crystal or in an optical lattice in the presence of binary alloy disorder are investigated. We employ the statistical dynamical mean-field theory, which incorporates both, fluctuations due to disorder and local correlations due to interaction, to solve the AndersonHubbard model. Localization due to disorder is studied by means of the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram consisting of disordered correlated metal, Anderson-Mott insulator, and band insulator.

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“…(20) defines the physical interacting Green's function, see Eq. (13). Up to this point the derivations are standard.…”

Section: Configuration-dependent Self-energy Functionalmentioning

confidence: 99%

“…With a proper scaling of the model parameters this limit preserves a highly non-trivial dynamics. 12,13 This distinguished mean-field theory, for the interaction part of the problem, is the dynamical mean-field theory (DMFT). 14,15,16,17 It gives the exact (local) interaction self-energy of the prototypical Hubbard model 18,19,20 in the D = ∞ limit.…”

Section: Introductionmentioning

confidence: 99%

Self-energy-functional theory for systems of interacting electrons with disorder

Potthoff

Balzer

2007

Phys. Rev. B

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Based on a functional-integral formalism, a generalization of the self-energy-functional theory (SFT) is proposed which is applicable to systems of interacting electrons with disorder. Similar to the pure case without disorder, a variational principle is set up which gives the physical (disorder) self-energy as a stationary point of the (averaged) grand potential. Although the resulting self-energy functional turns out to be more complicated, the formal structure of the theory can be retained since the unknown part of the functional is universal. This allows to construct nonperturbative and thermodynamically consistent approximations via searching for a stationary point on a restricted domain of the functional. The theory and the possible approximations are worked out for models with local interactions and local disorder. This results in a derivation of different mean-field approaches and various cluster extensions, including well-known concepts as the statistical dynamical mean-field theory, the molecular coherent-potential approximation and the dynamical cluster approximation. Due to the common formal framework provided by the SFT, one achieves a general systematization of dynamical approaches, i.e. approaches based on the spectrum of oneparticle excitations. New mean-field and new cluster schemes naturally appear in this framework and complement the existing ones. Their prospects for future applications are discussed.

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Controlled mean-field theory for disordered electronic systems: Single-particle properties

Cited by 93 publications

References 33 publications

Dynamical Mean-Field Theory

Dynamical Mean-Field Theory

Mott-Hubbard and Anderson metal-insulator transitions in correlated lattice fermions with binary disorder

Self-energy-functional theory for systems of interacting electrons with disorder

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