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Journal of Physics Conference Series

Quantum phases of Bose–Fermi mixtures in optical lattices

K Noda, Robert Peters, N. Kawakami, Thomas Pruschke

Published Jan 1, 2011• 3 citations
Publisher

Abstract

We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.

DOI
10.1088/1742-6596/273/1/012146

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We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.
We investigate many-body effects on a mixture of interacting bosons and fermions loaded in an optical lattice using a generalized dynamical mean-field theory combined with the numerical renormalization group. We show that strong correlation effects emerge in the presence of bosonic superfluidity, leading to a renormalized peak structure near the Fermi level in the density of states for fermions. Remarkably, this kind of strong renormalization appears not only in the metallic phase but also in the insulating phases of fermions such as in the empty- and filled-band limit. A systematic analysis of the relation between the quasiparticle weight and the strength of superfluidity reveals that the renormalization effect is indeed caused by the boson degrees of freedom. It is found that such renormalization is also relevant to a supersolid phase consisting of a density-wave ordering of fermions accompanied by bosonic superfluidity. This sheds light on the origin of the peak structure in the supersolid phase.
We give a detailed discussion of the recently developed generalized dynamical mean-field theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is nonperturbative and exact in infinite dimensions, and reliably describes the full range from weak to strong coupling. Like in conventional dynamical mean-field theory, the small parameter is 1/z1/z1/z, where zzz is the lattice coordination number. We apply the GDMFT scheme to a mixture of spinless fermions and bosons in an optical lattice. We investigate the possibility of a supersolid phase, focusing on the case of 1/2 filling for the fermions and 3/2 filling for the bosons.
We discuss the theory of mixtures of bosonic and fermionic atoms in periodic potentials at zero temperature. We derive a general Bose-Fermi Hubbard Hamiltonian in a one-dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean-field criterion for the onset of a bosonic superfluid transition. We investigate the ground-state properties of the mixture in the Gutzwiller formulation of mean-field theory, and present numerical studies of finite systems. The bosonic and fermionic density distributions and the onset of quantum phase transitions to demixing and to a bosonic Mott-insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasidegenerate ground states is related to a breaking of the mirror symmetry in the lattice.
We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.
We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are an important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign, and consequently the interspecies interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above, we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out the fermionic field provides an additional interaction that can decrease or increase bosonic coherence.
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.