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.
View Article and Find Full Text PDFThe 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.
View Article and Find Full Text PDFThe 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.
View Article and Find Full Text PDFThe 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.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFRecent 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.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
March 2007
We study the scaling properties of the solid-on-solid front of the infinite cluster in two-dimensional gradient percolation. We show that such an object is self-affine with a Hurst exponent equal to 23 up to a cutoff length approximately g{-4/7}, where g is the gradient. Beyond this length scale, the front position has the character of uncorrelated noise.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFPhys Rev Lett
September 2004
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.
View Article and Find Full Text PDFPhilos Trans A Math Phys Eng Sci
August 2004
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.
View Article and Find Full Text PDFUsing 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.
View Article and Find Full Text PDFWe 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.
View Article and Find Full Text PDFWe study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.
View Article and Find Full Text PDFWe present a simple criterion based on the Einstein relation for determining whether diffusion in systems governed by a generalized Langevin equation with long-range memory is normal, superdiffusive, or subdiffusive. We support our analysis with numerical simulations.
View Article and Find Full Text PDFIn 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.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
March 2002
We investigate numerically the failure process when two elastic media, one hard and one soft that have been glued together thus forming a common interface, are pulled apart. We present three main results: (1) The area distribution of simultaneously failing glue (bursts) follows a power law consistent with the theoretically expected exponent 2.5, (2) the maximum load and displacement before catastrophic failure scale as L(2) and L(0), respectively, where L is the linear size of the system, and (3) the area distribution of failed glue regions (clusters) is a power law with exponent -1.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
June 2001
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.
View Article and Find Full Text PDFWe study quantum phase transitions in the ground state of the two dimensional hard-core boson Hubbard Hamiltonian. Recent work on this and related models has suggested "supersolid" phases with simultaneous diagonal and off-diagonal long range order. We show numerically that, contrary to the generally held belief, the most commonly discussed "checkerboard" supersolid is thermodynamically unstable.
View Article and Find Full Text PDFWe propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free energy. The main consequence of the theory is that the average over randomness has to be taken after finding the critical point of each realization. To demonstrate these concepts, we study the finite-size scaling properties of the two-dimensional random-bond Ising model.
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