Pairing and Pair Superfluid Density in One-Dimensional Two-Species Fermionic and Bosonic Hubbard Models.

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in a uniform, i.e., with no confining potential, one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity; there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e., Bardeen-Cooper-Schrieffer (BCS) pairing, requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft-core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.

Charge Order in the Holstein Model on a Honeycomb Lattice.

The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin-liquid phase between the semimetal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo simulations to study the Holstein model on a honeycomb lattice and explore the role of electron- phonon interactions on Dirac fermions. We show that they give rise to charge-density-wave (CDW) order and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.

Competing supersolid and Haldane insulator phases in the extended one-dimensional bosonic Hubbard model.

The Haldane insulator is a gapped phase characterized by an exotic nonlocal 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 understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model 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, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.

Kondo screening and magnetism at interfaces.

The nature of magnetic order and transport properties near surfaces is a topic of great current interest. Here we model metal-insulator interfaces with a multilayer system governed by a tight-binding Hamiltonian in which the interaction is nonzero on one set of adjacent planes and zero on another. As the interface hybridization is tuned, magnetic and metallic properties undergo an evolution that reflects the competition between antiferromagnetism and (Kondo) singlet formation in a scenario similar to that occurring in heavy-fermion materials. For a few-layer system at intermediate hybridization, a Kondo insulating phase results, where magnetic order and conductivity are suppressed in all layers. As more insulating layers are added, magnetic order is restored in all correlated layers except that at the interface. Residual signs of Kondo physics are however evident in the bulk as a substantial reduction of the order parameter in the 2 to 3 layers immediately adjacent to the interfacial one. We find no signature of long-range magnetic order in the metallic layers.

Pure Mott phases in confined ultracold atomic systems.

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 numerical 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 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 in cold-atom experiments.

Determinant quantum monte carlo study of the orbitally selective mott transition.

We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two-band fermion Hubbard model using determinant quantum Monte Carlo (DQMC) simulations. We show that an orbitally selective Mott transition (OSMT) occurs in which the more weakly interacting band can be metallic despite complete localization of the strongly interacting band. The DQMC method allows us to test the validity of the use of a momentum independent self-energy which has been a central approximation in previous OSMT studies. In addition, we show that long range antiferromagnetic order (LRAFMO) is established in the insulating phase, similar to the single band, square lattice Hubbard Hamiltonian. Because the critical interaction strengths for the onset of insulating behavior are much less than the bandwidth of the itinerant orbital, we suggest that LRAFMO plays a key role in the transitions.

Magnetic and superfluid transitions in the one-dimensional spin-1 boson Hubbard model.

Recent progress in experiments on trapped ultracold atoms has made it possible to study the interplay between magnetism and superfluid-insulator transitions in the boson Hubbard model. We report on quantum Monte Carlo simulations of the spin-1 boson Hubbard model in the ground state. For antiferromagnetic interactions favoring singlets, we present exact numerical evidence that the superfluid-insulator transition is first (second) order for even (odd) Mott lobes. Inside even lobes, we search for nematic-to-singlet first order transitions. In the ferromagnetic case where transitions are all continuous, we map the phase diagram and show the superfluid to be ferromagnetic. We compare the quantum Monte Carlo phase diagram with a third order perturbation calculation.

Exact numerical study of pair formation with imbalanced fermion populations.

We present an exact quantum Monte Carlo study of the attractive one-dimensional Hubbard model with imbalanced fermion population. The pair-pair correlation function, which decays monotonically in the absence of polarization P, develops oscillations when P is nonzero, characteristic of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. The pair momentum distribution peaks at a momentum equal to the difference in the Fermi momenta. At strong coupling, the minority and majority momentum distributions are shown to be deformed, reflecting the presence of the other species and its Fermi surface. The FFLO oscillations survive the presence of a confining potential, and the local polarization at the trap center exhibits a marked dip, similar to that observed experimentally.

Quantum Monte Carlo study of an interaction-driven band-insulator-to-metal transition.

We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.

Supersolid phases in the one-dimensional extended soft-core bosonic Hubbard model.

We present results of quantum Monte Carlo simulations for the soft-core extended bosonic Hubbard model in one dimension exhibiting the presence of supersolid phases similar to those recently found in two dimensions. We find that in one and two dimensions, the insulator-supersolid transition has dynamic critical exponent z = 2 whereas the first order insulator-superfluid transition in two dimensions is replaced by a continuous transition with z = 1 in one dimension. We present evidence that this transition is in the Kosterlitz-Thouless universality class and discuss the mechanism behind this difference. The simultaneous presence of two types of quasi-long-range order results in two solitonlike dips in the excitation spectrum.

Phase coherence, visibility, and the superfluid-Mott-insulator transition on one-dimensional optical lattices.

We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et al. [Phys. Rev. Lett. 95, 050404 (2005); 10.1103/PhysRevLett.95.050404cond-mat/0507087]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that, as the interaction strength U is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than 1.

Phase separation in the two-dimensional bosonic Hubbard model with ring exchange.

We show that soft-core bosons in two dimensions with a ring exchange term exhibit a tendency for phase separation. This observation suggests that the thermodynamic stability of normal Bose liquid phases driven by ring exchange should be carefully examined.

Free-energy landscape and the critical velocity of superfluid films.

We briefly review some important properties of superfluid flow, especially the problem of critical velocity. We then present new numerical simulation results for a mesoscopic model of superfluids shedding light on the free-energy landscape, the critical velocity and the formation of vortices, which destroy the superflow when the velocity is high.

Local quantum criticality in confined fermions on optical lattices.

Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a nontrivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, which allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.

Mott domains of bosons confined on optical lattices.

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.

Distinguishing fractional and white noise in one and two dimensions.

We discuss the link between uncorrelated noise and the Hurst exponent for one- and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent H lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analyzing the correlations in two dimensions is necessary. For H>-1/2, a crossover regime leads to an systematic overestimate of the Hurst exponent.

Motion of grains down a bumpy surface.

We summarize in this article an extensive experimental and theoretical effort carried out to understand the behavior of a single ball when rolling down a bumpy surface. This may appear to be a simple problem but in fact is one that displays a rich variety of different behaviors which allow us to understand better dissipative systems such as granular media. Studies performed previously have shown that the motion of the single ball on the rough surface can be characterized by three different dynamic regimes according to the different values of the two control parameters, the inclination angle theta and the ratio Phi=R/r, where R is the radius of the rolling ball and r the radius of the glass beads which make up the rough surface. The three regimes are a decelerated regime A, a stationary regime B, characterized by a constant average velocity and a jumping regime C. This result was found to be independent of the composition of the rolling ball and the rough surface. It has been demonstrated that regime B is characterized by a viscous-like friction force that appears for specific parameter values. This friction force can be explained by a model whose central ingredient is the geometry of the surface. The trajectory of the ball in regime B can be pictured as a driven random walk motion where the fluctuations of the local velocities are due to collisions of the moving sphere and the surface grains. A detailed analysis of diffusive properties of the motion is discussed. (c) 1999 American Institute of Physics.