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arXiv:1103.0245 · Physical Review A

Phase diagram of the bosonic Kondo-Hubbard model

Michael Foss‐Feig, Ana María Rey

Published Nov 16, 2011• 16 citations

Abstract

We study a bosonic version of the Kondo lattice model with an onsite repulsion in the conduction band, implemented with alkali-metal atoms in two bands of an optical lattice. Using both weak- and strong-coupling perturbation theory, we find that at unit filling of the conduction bosons the superfluid-to-Mott-insulator transition should be accompanied by a magnetic transition from a ferromagnet (in the superfluid) to a paramagnet (in the Mott insulator). Furthermore, an analytic treatment of Gutzwiller mean-field theory reveals that quantum spin fluctuations induced by the Kondo exchange cause the otherwise continuous superfluid-to-Mott-insulator phase transition to be first order. We show that lattice separability imposes a serious constraint on proposals to exploit excited bands for quantum simulations, and discuss a way to overcome this constraint in the context of our model by using an experimentally realized nonseparable lattice. A method to probe the first-order nature of the transition based on collapses and revivals of the matter-wave field is also discussed.

DOI: 10.1103/physreva.84.053619

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We study, using quantum Monte Carlo simulations, the bosonic Kondo-Hubbard model in a two-dimensional square lattice. We explore the phase diagram and analyze the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight-binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.

We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2

XXZ

model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.

We study spin-1 bosons in an optical lattice under a magnetic field with the Gutzwiller approximation for the Bose-Hubbard model. Phase boundary curves between superfluids and Mott insulators depend continuously on the magnetic field, and this provides better results than those obtained with the perturbative mean-field approximation. The phase boundary curve as a function of magnetic field has a sharp cusp structure under certain circumstances. In superfluid phases, both the spin magnetizations and fluctuations in the total number of bosons show strong magnetic field dependence, which is related to the fact that both first-and second-order transitions appear on the phase boundary curve according to the magnetic field.

The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.

We study the Mott insulator--superfluid transition in a two-band boson Hubbard model, which can be mapped onto a spin-

1∕2

XY

model with spins coupled to an additional Ising degree of freedom. By using a modified mean field theory that includes the effects of phase fluctuations, we show that the transition is first order at both zero and finite temperatures. On the Mott insulator side, there may be reentrance in phase transition. These features are consequences of the underlying transition between competing defect poor and defect rich phases. The possible relevance of the model and our results to supersolid

^{4}\mathrm{He}

and cold bosonic atoms in optical lattices are discussed.

We investigate the superfluid--Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an

{F}_{g}=1

to

{F}_{e}=1

internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well as within the framework of perturbation theory.