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Physical Review B

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

Shi-Jian Gu, Junpeng Cao, Shu Chen, Hai-Qing Lin

Published Dec 14, 2009• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.80.224508

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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 SU(1\ensuremath∣1)\text{SU}(1\ensuremath{\mid}1)SU(1\ensuremath∣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 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.
We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase 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. We show that the static density correlations in these two regimes are markedly different.
We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.
We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase 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. We show that the static density correlations in these two regimes are markedly different.
We study ground-state phase diagrams and excitation spectra of Bose-Bose mixtures in an optical lattice by applying the Gutzwiller approximation to the two-component Bose-Hubbard model. A case of equal hoppings and equal intra-component interactions for both components is considered. Due to the existence of inter-component interaction, there appear several quantum phases, such as the superfluid, paired superfluid, and counterflow superfluid phases. We find that the transition from superfluid (SF) to Mott insulator (MI) with even filling factors can be of the first order for a wide range of the chemical potential. We calculate the excitation spectra as a useful probe to identify the quantum phases and the SF-to-MI transitions. In the excitation spectra of the SF phase, there are two gapless modes and a few gapful modes, which respectively correspond to phase and amplitude fluctuations of the order parameters. At the SF-to-MI transition point, we show that the energy gaps of certain amplitude modes reach zero for the second-order transition while they remain finite for the first-order one. Since the excitation spectrum can be measured by the Bragg scattering, we calculate the dynamical structure factor by using the linear response theory. We consider three types of density fluctuations, and show that the density fluctuations are coupled to different excitation branches in different quantum phases.
We study the Bose-Fermi mixture with infinite boson-boson repulsion and finite boson-fermion repulsion. Using a generalized Jordan-Wigner transformation, we show that the system can be mapped to a repulsive Hubbard model and thus can be solved exactly for the case with equal boson and fermion masses. Using the Bethe-ansatz solutions, we investigate the ground-state properties of the mixture system. Our results indicate that the system with commensurate filling n=1n=1n=1 is a charge insulator but still a superfluid with nonvanishing superfluid density. We also briefly discuss the case with unequal boson and fermion masses.