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 Bose-Hubbard Hamiltonian describes the competition between superfluidity and Mott insulating behavior at zero temperature and commensurate filling as the strength of the on-site repulsion is varied. Gapped insulating phases also occur at non-inte
ger densities as a consequence of longer ranged repulsive interactions. In this paper we explore the formation of gapped phases in coupled chains due instead to anisotropies $t_x eq t_y$ in the bosonic hopping, extending the work of Crepin {it et al.} [Phys. Rev. B 84, 054517 (2011)] on two coupled chains, where a gap was shown to occur at half filling for arbitrarily small interchain hopping $t_y$. Our main result is that, unlike the two-leg chains, for three- and four-leg chains, a charge gap requires a finite nonzero critical $t_y$ to open. However, these finite values are surprisingly small, well below the analogous values required for a fermionic band gap to open.
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.
The two dimensional square lattice hard-core boson Hubbard model with near neighbor interactions has a `checkerboard charge density wave insulating phase at half-filling and sufficiently large intersite repulsion. When doped, rather than forming a su
persolid phase in which long range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $hat x$ and $hat y$ directions, we conclude that phase separation still occurs.
We propose a novel scheme for confining atoms to optical lattices by engineering a spatially-inhomogeneous hopping matrix element in the Hubbard-model (HM) description, a situation we term off-diagonal confinement (ODC). We show, via an exact numeric
al solution of the boson HM with ODC, that this scheme possesses distinct advantages over the conventional method of confining atoms using an additional trapping potential, including the presence of incompressible Mott phases at commensurate filling and a phase diagram that is similar to the uniform HM. The experimental implementation of ODC will thus allow a more faithful realization of correlated phases of interest in cold atom experiments.
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength U (relative to the hopping parameter t) at half-filling and zero temperature, the syste
m undergoes a quantum phase transition at 5.0 < U_c/t < 5.1 from a semi-metal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half-filling, and increasing the interaction strength at finite but low temperature T, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered.
The interplay between magnetism and metal-insulator transitions is fundamental to the rich physics of the single band fermion Hubbard model (FHM). Recent progress in experiments on trapped ultra-cold atoms have made possible the exploration of simila
r effects in the boson Hubbard model (BHM). This paper reports Quantum Monte Carlo (QMC) simulations of the spin-1 BHM in the ground state. In the case of antiferromagnetic interactions, which favor singlet formation within the Mott insulator lobes, we present exact numerical evidence that the superfluid-insulator phase transition is first (second) order depending on whether the Mott lobe is even (odd). In the ferromagnetic case, the transitions are all continuous. We obtain the phase diagram in the case of attractive spin interactions and demonstrate the existence of the ferromagnetic superfluid. We also compare the QMC phase diagram with a third order perturbation calculation.
Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently, concerns
the properties of ultra-cold, optically trapped atoms. Of interest is how the superfluid-insulator transition is modified by the inhomogeneity, and, indeed, the extent to which a sharp transition survives at all. This paper explores a classical analog of these systems, the Blume-Capel model with a spatially varying single ion anisotropy and/or temperature gradient. We present results both for the nature of the critical properties and for the validity of the local density approximation which is often used to model the inhomogeneous case. We compare situations when the underlying uniform transition is first and second order.
Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the $(mu/U,t/U)$ phase diagram of t
he uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.
The single band, two dimensional Hubbard Hamiltonian has been extensively studied as a model for high temperature superconductivity. While Quantum Monte Carlo simulations within the dynamic cluster approximation are now providing considerable evidenc
e for a d-wave superconducting state at low temperature, such a transition remains well out of reach of finite lattice simulations because of the sign problem. We show here that a bilayer Hubbard model, in which one layer is electron doped and one layer is hole doped, can be studied to lower temperatures and exhibits an interesting signal of d-wave pairing. The results of our simulations bear resemblance to a recent report on the magnetic and superconducting properties of Ba$_2$Ca$_3$Cu$_4$O$_8$F$_2$ which contains both electron and hole doped CuO$_2$ planes. We also explore the phase diagram of bilayer models in which each sheet is at half-filling.
