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arXiv:cond-mat/0601496 · Physical Review B

Ground state of a mixture of two species of fermionic atoms in a one-dimensional optical lattice

Shi-Jian Gu, Rui Fan, Hai-Qing Lin

Published Sep 14, 2007• 24 citations
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Abstract

In this paper, we investigate the ground-state properties of a mixture of two species of fermionic atoms in a one-dimensional optical lattice, as described by the asymmetric Hubbard model. The quantum phase transition from density wave to phase separation is investigated by studying both the corresponding charge order parameter and quantum entanglement. A rigorous proof that even for the single-hole doping case, the density wave is unstable to the phase separation in the infinite $U$ limit, is given. Therefore, our results are quite instructive for both ongoing experiments on strongly correlated cold-atomic systems and traditional heavy fermion systems.

DOI
10.1103/physrevb.76.125107

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In this paper, we investigate the ground-state properties of a mixture of two species of fermionic atoms in a one-dimensional optical lattice, as described by the asymmetric Hubbard model. The quantum phase transition from density wave to phase separation is investigated by studying both the corresponding charge order parameter and quantum entanglement. A rigorous proof that even for the single-hole doping case, the density wave is unstable to the phase separation in the infinite UUU limit, is given. Therefore, our results are quite instructive for both ongoing experiments on strongly correlated cold-atomic systems and traditional heavy fermion systems.
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.
The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.
Ground-state properties of fermionic mixtures confined in a one-dimensional optical lattice are studied numerically within the spinless Falicov-Kimball model with a harmonic trap. A number of remarkable results are found. i) At low particle filling the system exhibits phase separation with heavy atoms in the center of the trap and light atoms in the surrounding regions. ii) Insulating phases always coexist with metallic phases. iii) Atomic-density waves are observed in the insulating regions for all particle fillings near the half-filled lattice case. iv) The variance of the local density exhibits universal behavior (independent of the particle filling, the Coulomb interaction and the strength of a confining potential) over the whole region of the local density values.
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 a two-species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with onsite interspecies repulsive interaction. Such a model can be realized in a cold-atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable interspecies interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various ppp-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures.
We study the quantum phase transitions in a two component Bose mixture in a one-dimensional optical lattice. The calculations have been performed in the framework of the extended Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain different phase transitions for the system for integer filling. When the interspecies on-site and the nearest-neighbor interactions are larger than the intraspecies on-site and also the nearest-neighbor interaction, the system exhibits a phase separated charge-density-wave order that is characterized by the two species being spatially separated and existing in the density-wave phases.