Self-consistent calculation of particle-hole diagrams on the Matsubara frequency: FLEX approximation

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling ($\rho = 0.40$), and for $T/t = 0.03$, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the a two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im$\Sigma(\vec{k},\omega) \approx w^2$ around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully selfconsistent and the non-selfconsistent ones give different results for the parameters considered here. However, they have similar global results for small densities.Comment: seven pages, nine figures as ps files. Accepted in Int. J. Modern Phys. C (1997

Stochastic properties of systems controlled by autocatalytic reactions II

We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X, X+X -> A+X, X -> B provided that the distribution of reacting particles in the system volume is uniform, i.e. the point model of reaction kinetics introduced in arXiv:cond-mat/0404402 can be applied. Assuming the number of substrate particles A to be kept constant by a suitable reservoir, we derived the forward Kolmogorov equation for the probability of finding n=0,1,... autocatalytic particles X in the system at a given time moment. We have shown that the stochastic model results in an equation for the mean value of autocatalytic particles X which differs strongly from the kinetic rate equation. It has been found that not only the law of the mass action is violated but also the bifurcation point is disappeared in the well-known diagram of X particle- vs. A particle-concentration. Therefore, speculations about the role of autocatalytic reactions in processes of the "natural selection" can be hardly supported.Comment: 17 pages, 6 figure

Boson Core Compressibility

Strongly interacting atoms trapped in optical lattices can be used to explore phase diagrams of Hubbard models. Spatial inhomogeneity due to trapping typically obscures distinguishing observables. We propose that measures using boson double occupancy avoid trapping effects to reveal key correlation functions. We define a boson core compressibility and core superfluid stiffness in terms of double occupancy. We use quantum Monte Carlo on the Bose-Hubbard model to empirically show that these quantities intrinsically eliminate edge effects to reveal correlations near the trap center. The boson core compressibility offers a generally applicable tool that can be used to experimentally map out phase transitions between compressible and incompressible states.Comment: 11 pages, 11 figure

Quasiparticle Self-Consistent GW Theory

In past decades the scientific community has been looking for a reliable first-principles method to predict the electronic structure of solids with high accuracy. Here we present an approach which we call the quasiparticle self-consistent GW approximation (QpscGW). It is based on a kind of self-consistent perturbation theory, where the self-consistency is constructed to minimize the perturbation. We apply it to selections from different classes of materials, including alkali metals, semiconductors, wide band gap insulators, transition metals, transition metal oxides, magnetic insulators, and rare earth compounds. Apart some mild exceptions, the properties are very well described, particularly in weakly correlated cases. Self-consistency dramatically improves agreement with experiment, and is sometimes essential. Discrepancies with experiment are systematic, and can be explained in terms of approximations made.Comment: 12 pages, 3 figure

Existence of Long-Range Order for Trapped Interacting Bosons

We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.Comment: 4 pages, 1 figure, RevTex4. Title changed at the request of editors; to appear in Phys. Rev. Letter

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called "Particle Linear Theory" (PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects -- in the linear regime -- of N-body simulations for which initial conditions have been set-up using these different lattices.Comment: 9 pages, 4 figures and 4 tables. Minor corrections to match published versio

k-dependent SU(4) model of high-temperature superconductivity and its coherent-state solutions

We extend the SU(4) model [1-5] for high-Tc superconductivity to an SU(4)k model that permits explicit momentum (k) dependence in predicted observables. We derive and solve gap equations that depend on k, temperature, and doping from the SU(4)k coherent states, and show that the new SU(4)k model reduces to the original SU(4) model for observables that do not depend explicitly on momentum. The results of the SU(4)k model are relevant for experiments such as ARPES that detect explicitly k-dependent properties. The present SU(4)k model describes quantitatively the pseudogap temperature scale and may explain why the ARPES-measured T* along the anti-nodal direction is larger than other measurements that do not resolve momentum. It also provides an immediate microscopic explanation for Fermi arcs observed in the pseudogap region. In addition, the model leads to a prediction that even in the underdoped regime, there exist doping-dependent windows around nodal points in the k-space, where antiferromagnetism may be completely suppressed for all doping fractions, permitting pure superconducting states to exist.Comment: 10 pages, 7 figure

GW approximation with self-screening correction

The \emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident in the case of the hydrogen atom. When applied to the hydrogen atom, the \emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.Comment: 9 pages, 2 figures; Submitted to Phys. Rev.

Dust ion-acoustic shocks in quantum dusty pair-ion plasmas

The formation of dust ion-acoustic shocks (DIASs) in a four-component quantum plasma whose constituents are electrons, both positive and negative ions and immobile charged dust grains, is studied. The effects of both the dissipation due to kinematic viscosity and the dispersion caused by the charge separation as well as the quantum tunneling due to the Bohm potential are taken into account. The propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) is governed by the Korteweg-de Vries-Burger (KdVB) equation which exhibits both oscillatory and monotonic shocks depending not only on the viscosity parameters, but also on the quantum parameter H (the ratio of the electron plasmon to the electron Fermi energy) and the positive to negative ion density ratio. Large amplitude stationary shocks are recovered for a Mach number exceeding its critical value. Unlike the small amplitude shocks, quite a smaller value of the viscosity parameter, H and the density ratio may lead to the large amplitude monotonic shock strucutres. The results could be of importance in astrophysical and laser produced plasmas.Comment: 15 pages, 5 figure