Self-Consistent Strong-Coupling-Perturbation Theory for the Anderson Model, Based on Wicks Theorem

A strong-coupling-perturbation theory around the Atomic Limit of the Anderson model with large $U$ for a localized $f$-orbital coupled to a conduction-electron band is presented. Although an auxiliary-particle representation is {\em not} used, application of the canonical Wick's theorem is possible and yields an expansion in the hybridization $V$ via dressed skeleton-Feynman diagrams. The Self-Consistent T-Approximation is constructed as a $\Phi$-derivable approximation. From a numerical solution of self-consistency equations the $f$-electron-excitation spectrum is investigated. Comparison to the Non-Crossing Approximation is made in virtue of exact formal relations and numerical results. An extension of this Feynman-diagram approach to the Anderson-lattice model is indicated, and application within the Local-Approximation scheme (limit of infinite spatial dimension) is given.Comment: 19 pages, revtex3.0, epsf, 11 figures included as .eps file

Auxiliary-Fermion Approach to Critical Fluctuations in the 2D Quantum AF Heisenberg Model

The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Q=1 on each lattice site, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T. This drawback, which is caused by overdamping, is overcome in a `minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths and in the short-range-order regime. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.Comment: Minor changes to match the published versio

On Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems: A New Approach Based on Wick's Theorem

A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect to the hybridization $V$ built on Feynman diagrams obeying standard rules is possible. The local correlations of the unperturbed system (the atomic limit) are included exactly through a two-particle vertex. No auxiliary particles are introduced into the theory. As an example and test the small energy scale and many-body resonance of the Kondo problem are reproduced analytically.Comment: To be presented at SCES'94, Amsterdam. Postscript file (5 pages) including 3 figures; ordinary latex-file plus postscript-figures available upon request (gnmlphgfrt

Signature of Spin Collective Mode in Local Tunneling Spectra of a d-wave Superconductor

We consider the influence of magnetic excitations on the local density of states in the d-wave superconductor. The magnetic susceptibility is calculated within the renormalized $t-t'-J$ model and its influence on the quasiparticle self-energy is considered using a minimal model originally proposed by Polkovnikov {\it et al.}[cond-mat/0203176]. We find the local density of states possess periodic components both along $(\pi,0)$ and $(\pi,\pi)$ directions with the associated wavevectors changing in magnitude as the quasiparticle energy is varied. Comparison with the STM experiment reveals that the calculated LDOS modulation is inconsistent with the measured data.Comment: Two figures separately attached as .jpg file

Spin susceptibility and the pi-excitation in underdoped cuprates

The dynamical spin susceptibility chi'' at wave vector (pi, pi) and the spectrum pi'' of the spin-triplet particle--particle excitation with center of mass momentum (pi, pi) (pi-excitation) are considered in the slave-boson formulation of the t--J-model. Propagators are calculated in a diagrammatic t-matrix approximation in the d-wave superconducting state for a wide doping range. The resulting spectra chi'' and pi'' both show a resonance at a doping dependent energy, in qualitative agreement with recent numerical cluster calculations. In underdoped systems, the peak position is comparable to that found in neutron scattering experiments. The peak in chi'' as well as pi'' is at low doping entirely caused by spin fluctuations, whereas the triplet particle--particle channel does not contribute as a collective mode.Comment: 3 pages, 4 eps-figures included, uses revtex, eps

Entrepreneurial talent and venture performance: A meta-analytic investigation of SMEs

AbstractAs the broad link between small and medium-sized firm activity and key policy goals such as employment or economic growth has become generally accepted, the conversation has focused on a more nuanced understanding of the entrepreneurial engines of economic activity. A significant body of research looking at antecedents to venture performance has identified that entrepreneurial talent variables account for meaningful differences in venture performance and that significant heterogeneity exists across performance measures. These are important issues for institutions and policy makers seeking to achieve specific economic goals (e.g., survival or growth of ventures, employment or revenue). Using meta-analysis, we integrate this work to view connections between aspects of entrepreneurial talent and different performance outcomes. Our investigation includes 50,045 firms (K of 183 studies) and summarizes 1002 observations of small and medium-sized firms. Analysis of these data yields an unexpectedly weak connection between education and performance. Furthermore, growth, scale (number of employees) and sales outcomes are significantly related to planning skills, while profit and other financial and qualitative measures are strongly connected with the network surrounding the firm founders. Moreover, we observe that entrepreneurial talent is more relevant in developing economies

Renormalized mean-field theory of the neutron scattering in cuprate superconductors

The magnetic excitation spectrum of the t-t'-J-model is studied in mean-field theory and compared to inelastic neutron-scattering (INS) experiments on YBCO and BSCCO superconductors. Within the slave-particle formulation the dynamical spin response is calculated from a renormalized Fermi liquid with an effective interaction ~J in the magnetic particle--hole channel. We obtain the so-called 41meV resonance at wave vector (pi,pi) as a collective spin-1 excitation in the d-wave superconducting state. It appears sharp (undamped), if the underlying Fermi surface is hole-like with a sufficient next-nearest-neighbor hopping t'<0. The double-layer structure of YBCO or BSCCO is not important for the resonance to form. The resonance energy \omega_{res} and spectral weight at optimal doping come out comparable to experiment. The observed qualitative behavior of \omega_{res} with hole filling is reproduced in the underdoped as well as overdoped regime. A second, much broader peak becomes visible in the magnetic excitation spectrum if the 2D wave-vector is integrated over. It is caused by excitations across the maximum gap, and in contrast to the resonance its energy is almost independent of doping. At energies above or below \omega_{res} the commensurate resonance splits into incommensurate peaks, located off (pi,pi). Below \omega_{res} the intensity pattern is of `parallel' type and the dispersion relation of incommensurate peaks has a negative curvature. This is in accordance with recent INS experiments on YBCO.Comment: 17pp including 14 figure