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

Potthoff, Michael; Balzer, M.

doi:10.1103/physrevb.75.125112

Cited by 29 publications

(53 citation statements)

References 89 publications

(158 reference statements)

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“…Another direct consequence of the alloy-band splitting is the fact that, if the alloy subband is effectively half-filled, a Mott-Hubbard metal-insulator transition can occur at non-integer filling [126]. The spectralweight transfer in correlated systems with binary-alloy disorder was also investigated away from the metal-insulator transition regime [127,128]. For the periodic Anderson model with the binary-alloy disorder analogous behavior was predicted [129].…”

Section: Electronic Correlations and Disordermentioning

confidence: 99%

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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%

“…The DMFT can easily be extended to study correlated lattice electrons with local disorder [112][113][114][115][116][117]8]. For this purpose a single-particle term with random local energies i is added to the Hubbard model, leading to the Anderson-Hubbard model…”

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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“…For a completely disordered system without any spatial symmetry, the self-energy is fully site-dependent. It this case α is a site index and the theory becomes equivalent with the so-called statistical DMFT [ 100,101,102,103].…”

Section: Real-space Dynamical Mean-field Theorymentioning

confidence: 99%

Static and dynamic variational principles for strongly correlated electron systems

Potthoff¹

2011

AIP Conference Proceedings

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Abstract. The equilibrium state of a system consisting of a large number of strongly interacting electrons can be characterized by its density operator. This gives a direct access to the groundstate energy or, at finite temperatures, to the free energy of the system as well as to other static physical quantities. Elementary excitations of the system, on the other hand, are described within the language of Green's functions, i.e. time-or frequency-dependent dynamic quantities which give a direct access to the linear response of the system subjected to a weak time-dependent external perturbation. A typical example is angle-revolved photoemission spectroscopy which is linked to the single-electron Green's function. Since usually both, the static as well as the dynamic physical quantities, cannot be obtained exactly for lattice fermion models like the Hubbard model, one has to resort to approximations. Opposed to more ad hoc treatments, variational principles promise to provide consistent and controlled approximations. Here, the Ritz principle and a generalized version of the Ritz principle at finite temperatures for the static case on the one hand and a dynamical variational principle for the single-electron Green's function or the self-energy on the other hand are introduced, discussed in detail and compared to each other to show up conceptual similarities and differences. In particular, the construction recipe for non-perturbative dynamic approximations is taken over from the construction of static mean-field theory based on the generalized Ritz principle. Within the two different frameworks, it is shown which types of approximations are accessible, and their respective weaknesses and strengths are worked out. Static Hartree-Fock theory as well as dynamical mean-field theory are found as the prototypical approximations.

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“…The mathematical concept for the treatment of disordered systems by means of VCA can be found in Ref. [48]. In this paper we present the first application of VCA for disordered systems and on top of that, as a new contribution to VCA theory, we extend the so-called Q-matrix formalism [47,49,50] to a formulation suitable for disordered systems.…”

Section: Variational Cluster Approachmentioning

confidence: 99%

“…Disorder is treated by introducing a reference system which shares, in addition to the interaction part, the disorder distribution with the physical system. The expression for the averaged grand-potential within VCA then reads [48]:…”

Section: Variational Cluster Approachmentioning

confidence: 99%

Excitations in disordered bosonic optical lattices

2010

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Spectral excitations of ultracold gases of bosonic atoms trapped in one-dimensional optical lattices with disorder are investigated by means of the variational cluster approach applied to the BoseHubbard model. Qualitatively different disorder distributions typically employed in experiments are considered. The computed spectra exhibit a strong dependence on the shape of the disorder distribution and the disorder strength. We compare alternative results for the Mott gap obtained from its formal definition and from the minimum peak distance, which is the quantity available from experiments.PACS numbers: 64.70. Tg, 73.43.Nq, 67.85.De, 03.75.Kk Interacting many-body systems with disorder are fascinating and challenging from both the experimental as well as the theoretical point of view. Understanding disordered bosonic systems has been of great interest ever since the pioneering works on the Bose-Hubbard (BH) model [1], which describes strongly interacting lattice bosons. Originally, the disordered BH model has been used to approximately describe various condensed matter systems, such as superfluid helium absorbed in porous media [2,3], superfluid films on substrates [4], and Josephson junction arrays [5]. However, seminal experiments on ultracold gases of atoms trapped in optical lattices shed new light on interacting bosonic many-body systems, as these systems provide a direct experimental realization of the BH model [6,7]. Intriguingly, these experiments allow to observe quantum many-body phenomena, such as the quantum phase transition from a superfluid to a Mott state [8]. The condensate of atoms can be driven across this phase transition by gradually increasing the laser beam intensity, which is directly related to the depth of the potential wells. There is a large experimental control over the system parameters such as the particle number or lattice depth, and in addition the parameters are tuneable over a wide range. While optical lattices provide a very clean experimental realization of strongly correlated lattice bosons, they can be used to study disordered systems on a very high level of control as well. Disorder can be added to the regular optical lattice by several techniques, such as by superposing additional optical lattices with shifted wavelength and beam angles [9][10][11][12][13][14], laser speckle fields [15][16][17][18], or including atoms of a different species acting as impurities [19].The disordered BH model has been widely investigated in the literature. Most of the work has been devoted to study the phase transitions occurring in the disordered BH model [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. At zero temperature the ground-state phase diagram depending on the chemical potential, the tunneling probability of the particles and the disorder * michael.knap@tugraz.at FIG. 1. (Color online)The periodic optical lattice potential is locally modified by disorder. In the illustration the disorder is bounded by ǫ * corresponding to a situation obtained by the superposition ...

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

Cited by 29 publications

References 89 publications

Dynamical Mean-Field Theory

Dynamical Mean-Field Theory

Static and dynamic variational principles for strongly correlated electron systems

Excitations in disordered bosonic optical lattices

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