Mixtures of correlated bosons and fermions: Dynamical mean-field theory for normal and condensed phases

Byczuk, Krzysztof; Vollhardt, D.

doi:10.1002/andp.200910362

Cited by 10 publications

(12 citation statements)

References 52 publications

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“…27 The virtue of developing a DMFT formalism for the Bose-Hubbard model lies in the possible extension of the formalism to models where known numerical methods fail. Prime examples are Bose-Fermi mixtures in two or three dimensions, [58][59][60][61] where previous calculations treated the spinless fermions within DMFT and the bosons at the mean-field level. 62 The formalism can also be generalized to mixtures with spinful fermions.…”

Section: Discussionmentioning

confidence: 99%

Dynamical mean-field theory for bosons

et al. 2011

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We discuss the recently developed bosonic dynamical mean-field (B-DMFT) framework, which maps a bosonic lattice model onto the selfconsistent solution of a bosonic impurity model with coupling to a reservoir of normal and condensed bosons. The effective impurity action is derived in several ways: (i) as an approximation to the kinetic energy functional of the lattice problem, (ii) using a cavity approach, and (iii) by using an effective medium approach based on adding a one-loop correction to the selfconsistently defined condensate. To solve the impurity problem, we use a continuous-time Monte Carlo algorithm based on a sampling of a perturbation expansion in the hybridization functions and the condensate wave function. As applications of the formalism we present finite temperature B-DMFT phase diagrams for the bosonic Hubbard model on a 3d cubic and 2d square lattice, the condensate order parameter as a function of chemical potential, critical exponents for the condensate, the approach to the weakly interacting Bose gas regime for weak repulsions, and the kinetic energy as a function of temperature.

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Section: Discussionmentioning

confidence: 99%

Dynamical mean-field theory for bosons

et al. 2011

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“…The B-DMFT is expected to be a valuable approximation scheme for the investigation of lattice bosons in situations where exact numerical computations are difficult to perform or inefficient, as in the case of bosons with disorder or many internal degrees of freedom, and for Bose-Fermi mixtures [143].…”

Section: Dmft For Correlated Bosons In Optical Latticesmentioning

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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“…Recently, a new framework of the bosonic DMFT (B-DMFT) was proposed by Byczuk and Vollhardt 21 in order to extend the idea of the DMFT to correlated lattice bosons and mixtures of bosons and fermions on a lattice. 22 In contrast to the fermionic DMFT (F-DMFT), the lattice model for bosons is mapped into a single-impurity problem with two species of bath spectra, those from the condensate bosons and those from the normal bosons, each of which should be self-consistently determined. The resulting effective bosonic impurity model has been solved by exact diagonalization (ED) method.…”

Section: Introductionmentioning

confidence: 99%

Numerical renormalization group for the bosonic single-impurity Anderson model: Dynamics

2010

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The bosonic single-impurity Anderson model ͑B-SIAM͒ is studied to understand the local dynamics of an atomic quantum dot ͑AQD͒ coupled to a Bose-Einstein condensation ͑BEC͒ state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization-group calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.

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Mixtures of correlated bosons and fermions: Dynamical mean-field theory for normal and condensed phases

Cited by 10 publications

References 52 publications

Dynamical mean-field theory for bosons

Dynamical mean-field theory for bosons

Dynamical Mean-Field Theory

Numerical renormalization group for the bosonic single-impurity Anderson model: Dynamics

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