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Bulletin of the American Physical Society

The Bose-Fermi Hubbard model in the light and heavy fermion limits

Alexander Mering, Dominik Muth, Michael Fleischhauer

Published May 28, 2008• 0 citations
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Abstract

We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.

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The Bose-Fermi Hubbard model in the light and heavy fermion limits

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We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.

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Quantum phase transition and elementary excitations of a Bose-Fermi mixture in a one-dimensional optical lattice

Shi-Jian Gu, Junpeng Cao, Shu Chen +1 more

The mixture of the scalar bosonic and the spinless or polarized fermionic cold atoms in the one-dimensional optical lattice is studied. The system is modeled by the Bose-Fermi-Hubbard Hamiltonian, which shows different behavior from that of the Bose-Hubbard or the Fermi-Hubbard models. Because the $\text{SU}(1\ensuremath{\mid}1)$-supersymmetric Bethe ansatz solution gives an excellent approximation to this kind of mixed cold atomic systems, the ground-state properties of the system such as the densities of state in the momentum space are obtained based on the Bethe ansatz. If the number of bosons is equal to that of fermions and the filling factor is 1, it is found that there exists a critical on-site interaction ${U}_{c}$. If $U<{U}_{c}$, the ground state of the system is in the superfluid phase, while if $U>{U}_{c}$, the ground state is in the insulating phase. The superfluid-insulator transition occurs at ${U}_{c}$. From the analysis of the superfluid density, the value of the critical point is determined as ${U}_{c}=2.79256$, which is larger than the ${U}_{c}=0$ for the Fermi-Hubbard model and smaller than the ${U}_{c}=3.28$ for the Bose-Hubbard model. The elementary excitations and effective Hamiltonian in the strong-coupling limit are also discussed.

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We study the ground-state properties of mixtures of strongly interacting bosonic atoms in an optical lattice. Applying a mean-field approximation to the Hubbard model for Bose-Bose mixtures, we calculate the densities and superfluid order parameters for both species. Due to the repulsive interaction between the two species, the system exhibits phase separation. First, in the extreme limit of the zero-hopping case, we derive analytical expressions for the phase boundaries. In particular, we derive the conditions for phase separation in the Mott insulator phase. We find that the conditions for the phase separation depend on the on-site interactions as well as the occupation numbers. In particular, we show that the coexisting state appears by varying the on-site inter-species interaction. We also show the phase diagram of the finite hopping case. Second, we calculate the spatial density profile of $^{87}$Rb-$^{41}$K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of $^{87}$Rb and varied the number of $^{41}$K, and used the parameters estimated by experiments. We show that the phase separated $^{87}$Rb-$^{41}$K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.

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Quantum degenerate Bose-Fermi mixtures on 1-D optical lattices

Pinaki Sengupta, Leonid P. Pryadko

We combine model mapping, exact spectral bounds, and a quantum Monte Carlo method to study the ground state phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional optical lattice. The exact boundary of the boson-demixing transition is obtained from the Bethe Ansatz solution of the standard Hubbard model. We prove that along a symmetry plane in the parameter space, the boson-fermion mixed phase is stable at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. The static density correlations are studied in these two limits and shown to have markedly different features.

arXiv:cond-mat/0512241•Dec 12, 2005•1 citation
We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.
We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.
The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.
We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model with dichotomic values of the stochastic variables. Phase boundaries between compressible, incompressible (Mott-insulating), and partially compressible phases are derived analytically within a generalized strong-coupling expansion and numerically using density matrix renormalization group (DMRG) methods. We show that first-order correlations in the partially compressible phases decay exponentially, indicating a glass-type behavior. Fluctuations within the respective incompressible phases are determined using perturbation theory and are compared to DMRG results.
The mixture of the scalar bosonic and the spinless or polarized fermionic cold atoms in the one-dimensional optical lattice is studied. The system is modeled by the Bose-Fermi-Hubbard Hamiltonian, which shows different behavior from that of the Bose-Hubbard or the Fermi-Hubbard models. Because the $\text{SU}(1\ensuremath{\mid}1)$-supersymmetric Bethe ansatz solution gives an excellent approximation to this kind of mixed cold atomic systems, the ground-state properties of the system such as the densities of state in the momentum space are obtained based on the Bethe ansatz. If the number of bosons is equal to that of fermions and the filling factor is 1, it is found that there exists a critical on-site interaction Uc{U}_{c}Uc​. If U<UcU<{U}_{c}U<Uc​, the ground state of the system is in the superfluid phase, while if U>UcU>{U}_{c}U>Uc​, the ground state is in the insulating phase. The superfluid-insulator transition occurs at Uc{U}_{c}Uc​. From the analysis of the superfluid density, the value of the critical point is determined as Uc=2.79256{U}_{c}=2.79256Uc​=2.79256, which is larger than the Uc=0{U}_{c}=0Uc​=0 for the Fermi-Hubbard model and smaller than the Uc=3.28{U}_{c}=3.28Uc​=3.28 for the Bose-Hubbard model. The elementary excitations and effective Hamiltonian in the strong-coupling limit are also discussed.
We study the ground-state properties of mixtures of strongly interacting bosonic atoms in an optical lattice. Applying a mean-field approximation to the Hubbard model for Bose-Bose mixtures, we calculate the densities and superfluid order parameters for both species. Due to the repulsive interaction between the two species, the system exhibits phase separation. First, in the extreme limit of the zero-hopping case, we derive analytical expressions for the phase boundaries. In particular, we derive the conditions for phase separation in the Mott insulator phase. We find that the conditions for the phase separation depend on the on-site interactions as well as the occupation numbers. In particular, we show that the coexisting state appears by varying the on-site inter-species interaction. We also show the phase diagram of the finite hopping case. Second, we calculate the spatial density profile of 87^{87}87Rb-41^{41}41K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of 87^{87}87Rb and varied the number of 41^{41}41K, and used the parameters estimated by experiments. We show that the phase separated 87^{87}87Rb-41^{41}41K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.
We combine model mapping, exact spectral bounds, and a quantum Monte Carlo method to study the ground state phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional optical lattice. The exact boundary of the boson-demixing transition is obtained from the Bethe Ansatz solution of the standard Hubbard model. We prove that along a symmetry plane in the parameter space, the boson-fermion mixed phase is stable at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. The static density correlations are studied in these two limits and shown to have markedly different features.