Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0908.4589 · Physical Review A

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

M. Iskin, James K. Freericks

Published Nov 24, 2009• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.80.053623

Related papers

Exactly solvable case of a one-dimensional Bose–Fermi mixture

Adilet Imambekov, Eugene Demler

We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.

arXiv:cond-mat/0505632•Physical Review A•Feb 24, 2006•90 citations

Mixtures of bosonic and fermionic atoms in optical lattices

Alexander P. Albus, Fabrizio Illuminati, Jens Eisert

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.

arXiv:cond-mat/0304223•Physical Review A•Aug 22, 2003•187 citations

Quantum phases of Bose–Fermi mixtures in optical lattices

K Noda, Robert Peters, N. Kawakami +1 more

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.

Journal of Physics Conference Series•Jan 1, 2011•3 citations

Generalized dynamical mean-field theory for Bose-Fermi mixtures in optical lattices

Irakli Titvinidze, Michiel Snoek, Walter Hofstetter

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 $1/z$, where $z$ 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.

arXiv:0810.1733•Physical Review B•Apr 6, 2009•27 citations

Quantum Many-Body Phenomena in Ultra Cold Atoms in Optical Lattices

Anzi Hu

Two models are discussed here to illustrate the quantum many-body phenomena in mixtures of ultra-cold atoms in optical lattices. The first model describes a mixture of two species of bosonic atoms of equal masses in optical lattices and the second describes a mixture of heavy bosonic atoms and light fermionic atoms in optical lattices. For both models, we assume the trap is present and use parameters typical in experiment. For the first model, the discussion is aimed at providing a thorough description of the collective behavior of the binary mixture in various interaction regions, with emphasis on two many-body phenomena, pairing and anti-pairing, as a result of the inter-species interaction. The pairing leads to a new type of superfluid order, called the paired superfluid (PSF) and the anti-pairing leads to another type of superfluid order, called the counter-flow superfluid (CFSF). In addition, we discuss the coexistence of charge density wave order with the three superfluid orders in the strong interaction region. We use both Luttinger liquid theory and the time evolving block decimation (TEBD) method to study this model in one dimension. The discussion is organized in three parts: the phase diagram and the correlation functions; the noise correlation functions; and the transport properties. Two phase diagrams are constructed to map the different orders in the parameter space. The correlation functions, include noise correlations, are carefully examined for the determination of the orders and for possible detection methods. In the end, the transport properties of the PSF and CFSF orders are studied through the dipole oscillation induced by trap displacement. For the second model, examining a mixture of heavy bosons and light fermions, the discussion is oriented toward determining the thermal properties of the mixture for attractive inter-species interactions. This work is motivated by experiments creating artificial molecules through optical and magnetic control of ultra-cold atoms. We use the strong coupling (SC) expansion method to evaluate the density profile, the onsite inter-species correlations, the density fluctuations and the entropy per particle. Analytical expressions are derived for all the quantities above as well as the partition function. To benchmark the accuracy, the SC calculations are compared with inhomogeneous dynamical mean field theory (IDMFT) and Monte Carlo (MC) simulation. From the calculations, we find that 1) the efficiency of creating pre-formed molecules is significantly increased by confining the mixtures onto optical lattices; 2) the temperature of the mixtures in optical lattices can be reliably estimated through the density gradient and the density fluctuations.

•Jan 1, 2023•0 citations

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

Krzysztof Byczuk, D. Vollhardt

Abstract We derive a dynamical mean‐field theory for mixtures of interacting bosons and fermions on a lattice (BF‐DMFT). The BF‐DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose‐Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF‐DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF‐DMFT we investigate two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one‐half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions.

arXiv:0906.4732•Annalen der Physik•Aug 17, 2009•14 citations
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.
We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.
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 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 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.
Two models are discussed here to illustrate the quantum many-body phenomena in mixtures of ultra-cold atoms in optical lattices. The first model describes a mixture of two species of bosonic atoms of equal masses in optical lattices and the second describes a mixture of heavy bosonic atoms and light fermionic atoms in optical lattices. For both models, we assume the trap is present and use parameters typical in experiment. For the first model, the discussion is aimed at providing a thorough description of the collective behavior of the binary mixture in various interaction regions, with emphasis on two many-body phenomena, pairing and anti-pairing, as a result of the inter-species interaction. The pairing leads to a new type of superfluid order, called the paired superfluid (PSF) and the anti-pairing leads to another type of superfluid order, called the counter-flow superfluid (CFSF). In addition, we discuss the coexistence of charge density wave order with the three superfluid orders in the strong interaction region. We use both Luttinger liquid theory and the time evolving block decimation (TEBD) method to study this model in one dimension. The discussion is organized in three parts: the phase diagram and the correlation functions; the noise correlation functions; and the transport properties. Two phase diagrams are constructed to map the different orders in the parameter space. The correlation functions, include noise correlations, are carefully examined for the determination of the orders and for possible detection methods. In the end, the transport properties of the PSF and CFSF orders are studied through the dipole oscillation induced by trap displacement. For the second model, examining a mixture of heavy bosons and light fermions, the discussion is oriented toward determining the thermal properties of the mixture for attractive inter-species interactions. This work is motivated by experiments creating artificial molecules through optical and magnetic control of ultra-cold atoms. We use the strong coupling (SC) expansion method to evaluate the density profile, the onsite inter-species correlations, the density fluctuations and the entropy per particle. Analytical expressions are derived for all the quantities above as well as the partition function. To benchmark the accuracy, the SC calculations are compared with inhomogeneous dynamical mean field theory (IDMFT) and Monte Carlo (MC) simulation. From the calculations, we find that 1) the efficiency of creating pre-formed molecules is significantly increased by confining the mixtures onto optical lattices; 2) the temperature of the mixtures in optical lattices can be reliably estimated through the density gradient and the density fluctuations.
Abstract We derive a dynamical mean‐field theory for mixtures of interacting bosons and fermions on a lattice (BF‐DMFT). The BF‐DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose‐Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF‐DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF‐DMFT we investigate two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one‐half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions.