Nonresonant inelastic light scattering in the Hubbard model

Inelastic light scattering from electrons is a symmetry-selective probe of the charge dynamics within correlated materials. Many measurements have been made on correlated insulators, and recent exact solutions in large dimensions explain a number of anomalous features found in experiments. Here we focus on the correlated metal, as described by the Hubbard model away from half filling. We can determine the B1g Raman response and the inelastic X-ray scattering along the Brillouin zone diagonal exactly in the large dimensional limit. We find a number of interesting features in the light scattering response which should be able to be seen in correlated metals such as the heavy fermions.Comment: 9 pages, 7 figures, typeset with ReVTe

Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model

The zero temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the Dynamical Mean Field Theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's Numerical Renormalization Group method. Results for quasiparticle weight, spectral function and self-energy are discussed for Bethe and hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance which appears to be isolated from the Hubbard bands.Comment: 4 pages, 3 eps-figures include

Magnetic and Dynamic Properties of the Hubbard Model in Infinite Dimensions

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the N\'eel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon as $n<1$. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.Comment: 32 page

Finite temperature numerical renormalization group study of the Mott-transition

Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T<T_c approx 0.02W (W: bandwidth) we find hysteresis with first-order transitions both at U_c1 (defining the insulator to metal transition) and at U_c2 (defining the metal to insulator transition), at T>T_c there is a smooth crossover from metallic-like to insulating-like solutions.Comment: 10 pages, 9 eps-figure

Dynamics of disordered heavy Fermion systems

Dynamics of the disordered heavy Fermion model of Dobrosavljevic et al. are calculated using an expression for the spectral function of the Anderson model which is consistent with quantum Monte Carlo results. We compute the self-energy for three distributions of Kondo scales including the distribution of Bernal et al. for UCu{5-x}Pd{x}. The corresponding low temperature optical conductivity shows a low-frequency pseudogap, a negative optical mass enhancement, and a linear in frequency transport scattering rate, consistent with results in Y{1-x}U{x}Pd{3} and UCu{5-x}Pd{x}.Comment: 5 pages, LaTeX and 4 PS figure

The low-energy scale of the periodic Anderson model

Wilson's Numerical Renormalization Group method is used to study the paramagnetic ground state of the periodic Anderson model within the dynamical mean-field approach. For the particle-hole symmetric model, which is a Kondo insulator, we find that the lattice Kondo scale T_0 is strongly enhanced over the impurity scale T_K; T_0/T_K ~ exp(1/3I), where I is the Schrieffer-Wolff exchange coupling. In the metallic regime, where the conduction band filling is reduced from one, we find characteristic signatures of Nozi\`eres exhaustion scenario, including a strongly reduced lattice Kondo scale, a significant suppression of the states available to screen the f-electron moment, and a Kondo resonance with a strongly enhanced height. However, in contrast to the quantitative predictions of Nozi\`eres, we find that the T_0 ~ T_K with a coefficient which depends strongly on conduction band filling.Comment: 11 pages, 9 figures, submitted to Phys. Rev.

A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots

The functional renormalization group provides an efficient description of the interplay and competition of correlations on different energy scales in interacting Fermi systems. An exact hierarchy of flow equations yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Practical implementations rely on suitable truncations of the hierarchy, which capture nonuniversal properties at higher energy scales in addition to the universal low-energy asymptotics. As a specific example we study transport properties through a single-level quantum dot coupled to Fermi liquid leads. In particular, we focus on the temperature T=0 gate voltage dependence of the linear conductance. A comparison with exact results shows that the functional renormalization group approach captures the broad resonance plateau as well as the emergence of the Kondo scale. It can be easily extended to more complex setups of quantum dots.Comment: contribution to Les Houches proceedings 2006, Springer styl

Diffractive Phenomena and Shadowing in Deep-Inelastic Scattering

Shadowing effects in deep-inelastic lepton-nucleus scattering probe the mass spectrum of diffractive leptoproduction from individual nucleons. We explore this relationship using current experimental information on both processes. In recent data from the NMC and E665 collaboration, taken at small x << 0.1 and Q^2 < 1 GeV^2, shadowing is dominated by the diffractive excitation and coherent interaction of low mass vector mesons. If shadowing is explored at small x > 1 GeV^2 as discussed at HERA, the situation is different. Here dominant contributions come from the coherent interaction of diffractively produced heavy mass states. Furthermore we observe that the energy dependence of shadowing is directly related to the mass dependence of the diffractive production cross section for free nucleon targets.Comment: 12 pages Latex, 8 figure

Polarized superfluid state in a three-dimensional fermionic optical lattice

We study ultracold fermionic atoms trapped in a three dimensional optical lattice by combining the real-space dynamical mean-field approach with continuous-time quantum Monte Carlo simulations. For a spin-unpolarized system we show results the density and pair potential profile in the trap for a range of temperatures. We discuss how a polarized superfluid state is spatially realized in the spin-polarized system with harmonic confinement at low temperatures and present the local particle density, local magnetization, and pair potential.Comment: 6 pages, 2 figure

Quantification of resting myocardial blood flow velocity in normal humans using real-time contrast echocardiography. A feasibility study

BACKGROUND: Real-time myocardial contrast echocardiography (MCE) is a novel method for assessing myocardial perfusion. The aim of this study was to evaluate the feasibility of a very low-power real-time MCE for quantification of regional resting myocardial blood flow (MBF) velocity in normal human myocardium. METHODS: Twenty study subjects with normal left ventricular (LV) wall motion and normal coronary arteries, underwent low-power real-time MCE based on color-coded pulse inversion Doppler. Standard apical LV views were acquired during constant IV. infusion of SonoVue(®). Following transient microbubble destruction, the contrast replenishment rate (β), reflecting MBF velocity, was derived by plotting signal intensity vs. time and fitting data to the exponential function; y (t) =A (1-e(-β(t-t0))) + C. RESULTS: Quantification was feasible in 82%, 49% and 63% of four-chamber, two-chamber and apical long-axis view segments, respectively. The LAD (left anterior descending artery) and RCA (right coronary artery) territories could potentially be evaluated in most, but contrast detection in the LCx (left circumflex artery) bed was poor. Depending on localisation and which frames to be analysed, mean values of [Image: see text] were 0.21–0.69 s(-1), with higher values in medial than lateral, and in basal compared to apical regions of scan plane (p = 0.03 and p < 0.01). Higher β-values were obtained from end-diastole than end-systole (p < 0.001), values from all-frames analysis lying between. CONCLUSION: Low-power real-time MCE did have the potential to give contrast enhancement for quantification of resting regional MBF velocity. However, the technique is difficult and subjected to several limitations. Significant variability in β suggests that this parameter is best suited for with-in patient changes, comparing values of stress studies to baseline