Mean Field Theory of the Mott-Anderson Transition

Dobrosavljević, V.; Kotliar, Gabriel

doi:10.1103/physrevlett.78.3943

Cited by 202 publications

(291 citation statements)

References 26 publications

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“…26. In our opinion a distinction in terminology is justified and useful: Firstly, RDMFT, leading to a set of self-consistency equations for a fixed disorder realization or any inhomogeneity, thus constituting a deterministic approach.…”

Section: Methods For Solving the Modelmentioning

confidence: 99%

“…Within statistical DMFT, this PDF is determined by an ensemble with a large number N of Green's functions. On the Bethe lattice, the hybridization function is given as sum over diagonal cavity Green's functions G 26,37,38,47 , i.e.…”

Section: A Statistical Dynamical Mean-field Theorymentioning

confidence: 99%

“…Our results are reappraised by a complementary investigation of the two-dimensional square lattice by means of real-space DMFT (RDMFT). 26,34,35 …”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, we employ the statistical dynamical mean-field theory (DMFT) 8,[26][27][28] to solve the Anderson-Hubbard Hamiltonian numerically. The statistical DMFT incorporates both strong correlations and disorder-induced fluctuations and is known to give accurate results for highdimensional systems, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Localization of correlated fermions in optical lattices with speckle disorder

et al. 2010

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Strongly correlated fermions in three-and two-dimensional optical lattices with experimentally realistic speckle disorder are investigated. We extend and apply the statistical dynamical mean-field theory, which treats local correlations non-perturbatively, to incorporate on-site and hopping-type randomness on equal footing. Localization due to disorder is detected via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram for experimentally realistic parameters and find a strong suppression of the correlationinduced metal insulator transition due to disorder. Our results indicate that the Anderson-Mott and the Mott insulator are not continuously connected due to the specific character of speckle disorder. Furthermore, we discuss the effect of finite temperature on the single-particle spectral function.

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Section: Methods For Solving the Modelmentioning

confidence: 99%

Section: A Statistical Dynamical Mean-field Theorymentioning

confidence: 99%

“…Our results are reappraised by a complementary investigation of the two-dimensional square lattice by means of real-space DMFT (RDMFT). 26,34,35 …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Localization of correlated fermions in optical lattices with speckle disorder

et al. 2010

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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]. Thereby a mean-field theory of Anderson localization can be derived which reproduces many of the expected features of the disorder-driven MIT for non-interacting electrons [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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Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

et al. 2023

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Methods to discretize the Hamiltonian of a topological insulator or topological superconductor, without giving up on the topological protection of the massless excitations (respectively, Dirac fermions or Majorana fermions) are reviewed. The method of tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent fermions propagate on a 2+1${2\bm {+}1}$ dimensional space‐time lattice with a tangent dispersion: tan2(bold-italicε/2)=tan2(kx/2)+tan2(ky/2)${\text{tan}^2 (\bm {\varepsilon }/2) \bm {=} \text{tan}^2 (k_x/2) \bm {+}\text{tan}^2 (k_y/2)}$ in dimensionless units. They avoid the fermion doubling lattice artefact that will spoil the topological protection, while preserving the fundamental symmetries of the Dirac Hamiltonian. Although the discretized Hamiltonian is nonlocal, as required by the fermion‐doubling no‐go theorem, it is possible to transform the wave equation into a generalized eigenproblem that is local in space and time. Applications that are discussed include Klein tunneling of Dirac fermions through a potential barrier, the absence of localization by disorder, the anomalous quantum Hall effect in a magnetic field, and the thermal metal of Majorana fermions.

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Mean Field Theory of the Mott-Anderson Transition

Cited by 202 publications

References 26 publications

Localization of correlated fermions in optical lattices with speckle disorder

Localization of correlated fermions in optical lattices with speckle disorder

Dynamical Mean-Field Theory

Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

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