We study, using quantum Monte-Carlo simulations, the bosonic Kondo-Hubbard model in a two dimensional square lattice. We explore the phase diagram and analyse the mobility of particles and magnetic properties. At unit filling, the transition from a p
aramagnetic 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 study the phase diagram of the one-dimensional bosonic Hubbard model with contact ($U$) and near neighbor ($V$) interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The par
ameter regime ($U$, $V$ and $mu$) where this phase exists and how it competes with other phases such as the supersolid (SS) phase, is incompletely understood. We use the Stochastic Green Function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $rho=1$, the SS phase exists for a very wide range of parameters (including commensurate fillings) and displays power law decay in the one body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane.
The Haldane Insulator is a gapped phase characterized by an exotic non-local order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understoo
d. Using the Stochastic Green Function (SGF) quantum Monte Carlo (QMC) and the Density Matrix Renormalization Group (DMRG), we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model (BHM) with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves (CDW), superfluid (SF), supersolid (SS) and the recently identified Haldane insulating (HI) phases. We show that the HI exists only at the tip of the unit filling CDW lobe and that there is a stable SS phase over a very wide range of parameters.
We study a model of interacting bosons that occupy the first excited p-band states of a two-dimensional optical lattice. In contrast to the much studied single band Bose-Hubbard Hamiltonian, this more complex model allows for non-trivial superfluid p
hases associated with condensation at non-zero momentum and staggered order of the orbital angular momentum in addition to the superfluid-Mott insulator transition. More specifically, we observe staggered orbital angular momentum order in the Mott phase at commensurate filling and superfluidity at all densities. We also observe a transition between the staggered angular momentum superfluid phase and a striped superfluid, with an alternation of the phase of the superfluid along one direction. The transition between these two phases was observed in a recent experiment, which is then qualitatively well described by our model.
The Stochastic Green Function (SGF) algorithm is able to simulate any Hamiltonian that does not suffer from the so-called sign problem. We propose a new global space-time update scheme for the SGF algorithm which, in addition to being simpler than th
e previous formulation, reduces auto-correlation times. Using as a concrete example the extended Bose-Hubbard model and the complex Hamiltonian with six-site ring-exchange interactions which was recently studied in ArXiv:1206.2566v1, we present a comprehensive review of the SGF algorithm and the new updating scheme. Measurements of non-trivial physical quantities are presented in detail. While the SGF algorithm works in the canonical ensemble by nature, we give a simple extension that allows us to perform simulations in the grand-canonical ensemble too. We also discuss an optimized implementation which allows for access to large system sizes.
We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations and focus on finite temperature effects. We show in two different cases, ferro- and antiferromagnetic spin-spin interactions,
that the phase diagram is composed of solid Mott phases, liquid phases and superfluid phases. In the antiferromagnetic case, the superfluid (SF) is polarized while the Mott insulator (MI) and normal Bose liquid (NBL) phases are not. On the other hand, in the ferromagnetic case, none of the phases is polarized. The superfluid-liquid transition is of the Berezinsky-Kosterlitz-Thouless type whereas the solid-liquid passage is a crossover.
We use Quantum Monte Carlo (QMC) simulations to study the pairing mechanism in a one-dimensional fermionic system governed by the Hubbard model with attractive contact interaction and with imbalance between the two spin populations. This is done for
the uniform system and also for the system confined in a harmonic trap to compare with experiments on confined ultra-cold atoms. In the uniform case we determine the phase diagram in the polarization-temperature plane and find that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is robust and persists to higher temperature for higher polarization. In the confined case, we also find that the FFLO phase is stabilized by higher polarization and that it is within the range of detection of experiments currently underway.
Quantum Monte Carlo (QMC) techniques are used to provide an approximation-free investigation of the phases of the one-dimensional attractive Hubbard Hamiltonian in the presence of population imbalance. The temperature at which the Fulde-Ferrell-Larki
n-Ovchinnikov (FFLO) phase is destroyed by thermal fluctuations is determined as a function of the polarization. It is shown that the presence of a confining potential does not dramatically alter the FFLO regime, and that recent experiments on trapped atomic gases likely lie just within the stable temperature range.
