We obtain the ground-state quantum phase diagram for a two-species Bose mixture in a one-dimensional optical lattice using the finite-size density-matrix renormalization group method. We discuss our results for different combinations of inter- and intraspecies interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are a superfluid and a Mott insulator, and a phase separation where the two different species reside in spatially separate regions. The spatially separated phase is further classified into phase-separated superfluid and Mott insulator. The phase separation appears for all the fillings we have considered, whenever the interspecies interaction is slightly larger than the intraspecies interactions.
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 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 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
87Rb-
41K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of
87Rb and varied the number of
41K, and used the parameters estimated by experiments. We show that the phase separated
87Rb-
41K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.
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.
We use the finite-size, density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional
(d=1) extended Bose-Hubbard model for density $\ensuremath{\rho}=1$ in the $U\ensuremath{-}V$ plane, where
U and
V are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: superfluid (SF), Mott insulator (MI), and mass-density-wave (MDW). For small values of
U and
V, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed, finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional Ising characters. For large values of
U and
V we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF, and MI-MDW phase boundaries join at a bicritical point at $(U,V)=(8.5\ifmmode\pm\else\textpm\fi{}0.05,4.75\ifmmode\pm\else\textpm\fi{}0.05)$.