An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.Comment: 19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof

Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

Dynamical correlations in multiorbital Hubbard models: Fluctuation-exchange approximations

We study the two band degenerate Hubbard model using the Fluctuation Exchange approximation (FLEX) method and compare the results with Quantum Monte-Carlo calculations. Both the self-consistent and the non-self-consistent versions of the FLEX scheme are investigated. We find that, contrary to the one band case, in the multiband case, good agreement with the Quantum Monte-Carlo results is obtained within the electron-electron T-matrix approximation using the full renormalization of the one-particle propagators. The crossover to strong coupling and the formation of satellites is more clearly visible in the non-self-consistent scheme. Finally we discuss the behavior of the FLEX for higher orbital degeneracy.Comment: 18 pages with 12 PS figure

Temporal and spatial variability in stable isotope ratios of SPM link to local hydrography and longer term SPM averages suggest heavy dependence of mussels on nearshore production

Temporal changes in hydrography affect suspended particulate matter (SPM) composition and distribution in coastal systems, potentially influencing the diets of suspension feeders. Temporal variation in SPM and in the diet of the mussel Perna perna, were investigated using stable isotope analysis. The δ13C and δ15 N ratios of SPM, mussels and macroalgae were determined monthly, with SPM samples collected along a 10 km onshore–offshore transect, over 14 months at Kenton-on-Sea, on the south coast of South Africa. Clear nearshore (0 km) to offshore (10 km) carbon depletion gradients were seen in SPM during all months and extended for 50 km offshore on one occasion. Carbon enrichment of coastal SPM in winter (June–August 2004 and May 2005) indicated temporal changes in the nearshore detrital pool, presumably reflecting changes in macroalgal detritus, linked to local changes in coastal hydrography and algal seasonality. Nitrogen patterns were less clear, with SPM enrichment seen between July and October 2004 from 0 to 10 km. Nearshore SPM demonstrated cyclical patterns in carbon over 24-h periods that correlated closely with tidal cycles and mussel carbon signatures, sampled monthly, demonstrated fluctuations that could not be correlated to seasonal or monthly changes in SPM. Macroalgae showed extreme variability in isotopic signatures, with no discernable patterns. IsoSource mixing models indicated over 50% reliance of mussel tissue on nearshore carbon, highlighting the importance of nearshore SPM in mussel diet. Overall, carbon variation in SPM at both large and small temporal scales can be related to hydrographic processes, but is masked in mussels by long-term isotope integration

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file

Fermi and non-Fermi liquid behavior in quantum impurity systems: Conserving slave boson theory

The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N)xSU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Taking the Anderson model as an example, these lectures first give an introduction to the auxiliary boson method to describe correlated systems governed by a strong, short-range electronic repulsion. It is then shown how to include the relevant low-lying excitations (coherent spin flip and charge fluctuation processes), while preserving the local gauge symmetry of the model. This amounts to a conserving T-matrix approximation (CTMA). We prove a cancellation theorem showing that the CTMA incorporates all leading and subleading infrared singularities at any given order in a self-consistent loop expansion of the free energy. As a result, the CTMA recovers the correct infrared behavior of the auxiliary particle propagators, indicating that it correctly describes both the Fermi and the non-Fermi regimes of the Anderson model.Comment: 37 pages, LaTeX, style file included, 10 postscript figures; to appear in Proceedings of the XXXVIII Cracow School of Theoretical Physics, Zakopane, Poland, June 1-10, 199

Effects of epibiosis on consumer-prey interactions

In many benthic communities predators play a crucial role in the population dynamics of their prey. Surface characteristics of the prey are important for recognition and handling by the predator. Because the establishment of an epibiotic assemblage on the surface of a basibiont species creates a new interface between the epibiotized organism and its environment, we hypothesised that epibiosis should have an impact on consumer-prey interactions. In separate investigations, we assessed how epibionts on macroalgae affected the susceptibility of the latter to herbivory by the urchin Arbacia punctulata and how epibionts on the blue mussel Mytilus edulis affected its susceptibility to predation by the shore crab Carcinus maenas. Some epibionts strongly affected consumer feeding behavior. When epibionts were more attractive than their host, consumer pressure increased. When epibionts were less attractive than their host or when they were repellent, consumer pressure decreased. In systems that are controlled from the top-down, epibiosis can strongly influence community dynamics. For the Carcinus/Mytilus system that we studied, the insitu distribution of epibionts on mussels reflected the epibiosis-determined preferences of the predator. Both direct and indirect effects are involved in determining these epibiont-prey-consumer interactions

Unified description of Fermi and non-Fermi liquid behavior in a conserving slave boson approximation for strongly correlated impurity models

We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the Kondo limit the bound state contributions are unimportant.Comment: 4 pages, Latex, 3 postscript figures included Final version with minor changes in wording, to appear in Phys.Rev.Let

Universality class of non-Fermi liquid behavior in mixed valence systems

A generalized Anderson single-impurity model with off-site Coulomb interactions is derived from the extended three-band Hubbard model, originally proposed to describe the physics of the copper-oxides. Using the abelian bosonization technique and canonical transformations, an effective Hamiltonian is derived in the strong coupling limit, which is essentially analogous to the Toulouse limit of the ordinary Kondo problem. In this limit, the effective Hamiltonian can be exactly solved, with a mixed valence quantum critical point separating two different Fermi liquid phases, {\it i.e.} the Kondo phase and the empty orbital phase. In the mixed valence quantum critical regime, the local moment is only partially quenched and X-ray edge singularities are generated. Around the quantum critical point, a new type of non-Fermi liquid behavior is predicted with an extra specific heat $C_{imp}\sim T^{1/4}$ and a singular spin-susceptibility $\chi_{imp}\sim T^{-3/4}$. At the same time, the effective Hamiltonian under single occupancy is transformed into a resonant-level model, from which the correct Kondo physical properties (specific heat, spin susceptibility, and an enhanced Wilson ratio) are easily rederived. Finally, a brief discussion is given to relate these theoretical results to observations in $UPd_xCu_{5-x}$ ($x=1,1.5$) alloys, which show single-impurity critical behavior consistent with our predictions.Comment: 26 pages, revtex, no figure. Some corrections have been made, but the basic results are kept. To be published in Physical Review

Vertex-corrected perturbation theory for the electron-phonon problem with non-constant density of states

A series of weak-coupling perturbation theories which include the lowest-order vertex corrections are applied to the attractive Holstein model in infinite dimensions. The approximations are chosen to reproduce the iterated perturbation theory in the limit of half-filling and large phonon frequency (where the Holstein model maps onto the Hubbard model). Comparison is made with quantum Monte Carlo solutions to test the accuracy of different approximation schemes.Comment: 31 pages, 15 figures, typeset in ReVTe