Universal properties of hard-core bosons confined on one-dimensional lattices

Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation $\lambda_{\eta}$ of the natural orbitals for large-$\eta$ at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.Comment: Revtex file, 5 pages, 5 figures. Content and references added. Published versio

Gauge Theory for a Doped Antiferromagnet in a Rotating Reference-Frame

We study a doped antiferromagnet (AF) using a rotating reference-frame. Whereas in the laboratory reference-frame with a globally fixed spin-quantization axis (SQA) the long-wavelength, low-energy physics is given by the O(3) non-linear $\sigma$-model with current-current interactions between the fermionic degrees of freedom and the order-parameter field for the spin-background, an alternative description in form of an U(1) gauge theory can be derived by choosing the SQA defined by the local direction of the order-parameter field via a SU(2) rotation of the fermionic spinor. Within a large-$N$ expansion of this U(1) gauge theory we obtain the phase diagram for the doped AF and identify the relevant terms due to doping that lead to a quantum phase transition at $T=0$ from the antiferromagnetically ordered N\'eel phase to the quantum-disordered (QD) spin-liquid phase. Furthermore, we calculate the propagator of the corresponding U(1) gauge field, which mediates a long-range transverse interaction between the bosonic and fermionic fields. It is found that the strength of the propagator is proportional to the gap of the spin-excitations. Therefore, we expect as a consequence of this long-range interaction the formation of bound states when the spin-gap opens, i.e.\ in the QD spin-liquid phase. The possible bound states are spin-waves with a (spin-) gap in the excitation spectrum, spinless fermions and pairs of fermions. Thus, an alternative picture for charge-spin separation emerges, with composite charge-separated excitations. Moreover, the present treatment shows an intimate connection between the opening of the spin-gap and charge-spin separation as well as pairing.Comment: 13 pages, also available at http://www.physik.uni-augsburg.de/theo2/Publications

Quantum disordered phase in a doped antiferromagnet

A quantitative description of the transition to a quantum disordered phase in a doped antiferromagnet is obtained with a U(1) gauge-theory, where the gap in the spin-wave spectrum determines the strength of the gauge-fields. They mediate an attractive long-range interaction whose possible bound-states correspond to charge-spin separation and pairing.Comment: 11 pages, LaTex, chris-preprint-1994-

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

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

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