Strong-coupling solution of the bosonic dynamical mean-field theory

We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization function of normal bosons around the atomic limit. The solution is used to compute the phase diagram of the bosonic Hubbard model for different lattices. We compare our results with numerical solutions of the B-DMFT equations and numerically exact methods, respectively. The very good agreement with those numerical results demonstrates that our approach captures the essential physics of correlated bosons both in the Mott insulator and in the superfluid phase. Close to the transition into the superfluid phase the momentum distribution function at zero momentum is found to be strongly enhanced already in the normal phase. The linked-cluster expansion also allows us to compute dynamical properties such as the spectral function of bosons. The evolution of the spectral function across the transition from the normal to the superfluid phase is seen to be characteristically different for the interaction driven and density driven transition, respectively.Comment: 8 pages, 6 figure

T-matrix formulation of real-space dynamical mean-field theory and the Friedel sum rule for correlated lattice fermions

We formulate real-space dynamical mean-field theory within scattering theory. Thereby the Friedel sum rule is derived for interacting lattice fermions at zero temperature.Comment: 7 pages, no figures, extended and corrected versio

NRG for the bosonic single-impurity Anderson model: Dynamics

The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization group (NRG) 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.Comment: 12 pages, 13 figure

Spin-selective localization of correlated lattice fermions

The interplay between local, repulsive interactions and disorder acting only on one spin orientation of lattice fermions ("spin-dependent disorder") is investigated. The nonmagnetic disorder vs. interaction phase diagram is computed using Dynamical Mean-Field Theory in combination with the geometric average over disorder. The latter determines the typical local density of states and is therefore sensitive to Anderson localization. The effect of spin-dependent disorder is found to be very different from that of conventional disorder. In particular, it destabilizes the metallic solution and leads to a novel spin-selective, localized phase at weak interactions and strong disorder

Multitude of phases in correlated lattice fermion systems with spin-dependent disorder

The magnetic phases induced by the interplay between disorder acting only on particles with a given spin projection ("spin-dependent disorder") and a local repulsive interaction is explored. To this end the magnetic ground state phase diagram of the Hubbard model at half-filling is computed within dynamical mean-field theory combined with the geometric average over disorder, which is able to describe Anderson localization. Five distinct phases are identified: a ferromagnetically polarized metal, two types of insulators, and two types of spin-selective localized phases. The latter four phases possess different long-range order of the spins. The predicted phase diagram may be tested experimentally using cold fermions in optical lattices subject to spin-dependent random potentials.Comment: 8 pages, 9 figures, revised versio

Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices

We theoretically analyze Fermi-Bose mixtures consisting of light fermions and heavy bosons that are loaded into optical lattices (ignoring the trapping potential). To describe such mixtures, we consider the Fermi-Bose version of the Falicov-Kimball model on a periodic lattice. This model can be exactly mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature for all parameter space as long as the mixture is thermodynamically stable. We employ dynamical mean-field theory to investigate the evolution of the Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral moment sum rules for the retarded Green's function and self-energy, and use them to benchmark the accuracy of our numerical calculations, as well as to reduce the computational cost by exactly including the tails of infinite summations or products. We show how the occupancy of the bosons, single-particle many-body density of states for the fermions, momentum distribution, and the average kinetic energy evolve with temperature. We end by briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball model in ultracold atomic systems.Comment: 10 pages with 4 figure

Momentum distribution and ordering in mixtures of ultracold light and heavy fermionic atoms

The momentum distribution is one of the most important quantities which provides information about interactions in many-body systems. At the same time it is a quantity that can easily be accessed in experiments on ultracold atoms. In this paper, we consider mixtures of light and heavy fermionic atoms in an optical lattice described effectively by the Falicov-Kimball model. Using a Monte Carlo method, we study how different ordered density-wave phases can be detected by measurement of the momentum distribution of the light atoms. We also demonstrate that ordered phases can be seen in Bragg scattering experiments. Our results indicate that the main factor that determines the momentum distribution of the light atoms is the trap confinement. On the other hand, the pattern formed by the heavy atoms seen in the Bragg scattering experiments is very sensitive to the temperature and possibly can be used in low-temperature thermometry.Comment: 10 pages, 11 figure

From the Cooper problem to canted supersolids in Bose-Fermi mixtures

We calculate the phase diagram of the Bose-Fermi Hubbard model on the 3d cubic lattice at fermionic half filling and bosonic unit filling by means of single-site dynamical mean-field theory. For fast bosons, this is equivalent to the Cooper problem in which the bosons can induce s-wave pairing between the fermions. We also find miscible superfluid and canted supersolid phases depending on the interspecies coupling strength. In contrast, slow bosons favor fermionic charge density wave structures for attractive fermionic interactions. These competing instabilities lead to a rich phase diagram within reach of cold gas experiments.Comment: 5 pages, 4 figures; replaced with published versio