Phase diagram of the three-dimensional Hubbard model at half filling

We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Neel temperature T_N is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above T_N is determined using the electronic compressibility as criterion.Comment: 6 pages, 6 figures, to be published in Eur. Phys. J. B (2000

Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices

Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulator transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.Comment: RevTex file, 13 pages, 19 figures, published versio

Time evolution of one-dimensional Quantum Many Body Systems

The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one-dimensional systems. We describe recent developments in the construction of numerical schemes for general (one-dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest-neighbor-interaction and investigate their accuracy by comparing with exact results.Comment: Contribution for the conference proceedings of the "IX. Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors" held in Vietri sul Mare (Salerno, Italy) in October 200

Supersolids in confined fermions on one-dimensional optical lattices

Using quantum Monte Carlo simulations, we show that density-density and pairing correlation functions of the one-dimensional attractive fermionic Hubbard model in a harmonic confinement potential are characterized by the anomalous dimension $K_\rho$ of a corresponding periodic system, and hence display quantum critical behavior. The corresponding fluctuations render the SU(2) symmetry breaking by the confining potential irrelevant, leading to structure form factors for both correlation functions that scale with the same exponent upon increasing the system size, thus giving rise to a (quasi)supersolid.Comment: 4 pages, 5 figures, published versio

Counterflow Extension for the F.A.S.T.-Model

The F.A.S.T. (Floor field and Agent based Simulation Tool) model is a microscopic model of pedestrian dynamics, which is discrete in space and time. It was developed in a number of more or less consecutive steps from a simple CA model. This contribution is a summary of a study on an extension of the F.A.S.T-model for counterflow situations. The extensions will be explained and it will be shown that the extended F.A.S.T.-model is capable of handling various counterflow situations and to reproduce the well known lane formation effect.Comment: Contribution to Crowds and Cellular Automata Workshop 2008. Accepted for publication in "Cellular Automata -- 8th International Conference on Cellular Automata for Research and Industry, ACRI 2008, Yokohama, Japan, September 23-26, Springer 2008, Proceedings

Time evolution of correlations in strongly interacting fermions after a quantum quench

Using the adaptive time-dependent density matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.Comment: Published version; minor changes, references adde

Cooperative effect of phonons and electronic correlations for superconductivity in cobaltates

We propose that unconventional superconductivity in hydrated sodium cobaltate $Na_xCoO_2$ results from an interplay of electronic correlations and electron-phonon interactions. On the basis of the $t-V$ model plus phonons we found evidences for a) unconventional superconductivity, b) realistic values of $T_c$ and c) the dome shape existing near $x \sim 0.35$. This picture is obtained for $V$ close to the critical Coulomb repulsion $V_c$ which separates the uniform Fermi liquid from $\sqrt{3} \times \sqrt{3}$ CDW ordered phase.Comment: 4 pages, 3 figure

Mott Domains of Bosons Confined on Optical Lattices

In the absence of a confining potential, the boson Hubbard model in its ground state is known to exhibit a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong on-site repulsion. In this paper, we use quantum Monte Carlo simulations to study the ground state of the one dimensional bosonic Hubbard model in a trap. We show that some, but not all, aspects of the Mott insulating phase persist when a confining potential is present. The Mott behavior is present for a continuous range of incommensurate fillings, a very different situation from the unconfined case. Furthermore the establishment of the Mott phase does not proceed via a quantum phase transition in the traditional sense. These observations have important implications for the interpretation of experimental results for atoms trapped on optical lattices. Initial results show that, qualitatively, the same results persist in higher dimensions.Comment: Revtex file, five figures, include

Quantum phase transitions in the Kane-Mele-Hubbard model

We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard U is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.Comment: 13 pages, 10 figures; final version; new Figs. 4(b) and 8(b