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

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

An exploration of impaired walking dynamics and fatigue in Multiple Sclerosis

BACKGROUND: Physical disability in multiple sclerosis (MS) is frequently characterized by impaired ambulation. Although walking tests have been successfully employed to assess walking ability in MS patients, data analytic procedures have predominantly relied on result-oriented parameters (e.g. total distance covered during a given amount of time), whereas process-oriented, dynamic walking patterns have mostly been ignored. This is striking, since healthy individuals have been observed to display a stereotypical U-shaped pattern of walking speed during timed walking, characterized by relatively high speed during the initial phase, subsequent slowing and final acceleration. Objective of the current study was to test the utility of the 6 min Walk (6MW) and the 12 min Walk (12MW) for revealing putatively abnormal temporal dynamic features of walking in MS. METHODS: A group of 37 MS patients was divided into subgroups with regard to their level of disability analyzed with the Expanded Disability Status Scale (EDSS; Mild MS Group, n = 20, EDSS 0 – 3.5; Moderate MS Group, n = 17, EDSS 4 – 5). Subsequently, both groups were compared to age-matched healthy controls (n = 25) on both tests with regard to result-oriented characteristics (mean walking speed), as well as dynamic features (mean decline in walking speed, degree of observed U-shape). RESULTS: Both MS groups showed a significantly lower mean walking speed than healthy controls, independent of test duration. Compared to controls, the Moderate MS Group also slowed down more rapidly throughout both tests. The same pronounced decline in walking speed was observed for the Mild MS Group in case of the 12MW. Additionally, for both MS groups an attenuated U-shaped velocity pattern was observed relative to controls in the 6MW. Patients' subjective fatigue scores were more strongly correlated with the decline in walking speed than with the common parameter of mean walking speed in the 6MW. CONCLUSIONS: MS patients display abnormal dynamics in their walking patterns. A pronounced linear decline in walking speed can be identified with the 12MW even in MS patients with seemingly mild disability. Similarly, the 6MW can be used to assess an abnormal walking profile. Particularly the linear decline in walking speed on this test shows a more robust association with subjective fatigue than mean walking speed. Dynamic walking parameters may hence represent valuable clinical features, serving as surrogate measures of motor fatigue. Future studies are needed to verify their prognostic value

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

A partition functional and thermodynamic properties of the infinite-dimensional Hubbard model

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin-symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature $T^\star$. We attribute this anomaly to the appearance of the Hubbard pseudo-gap. The specific heat also shows a peak near $T^\star$. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around $T^\star$ and has a rough linear temperature dependence above $T^\star$.Comment: 18 pages, 6 figures upon request, latex, (to appear in Phys. Rev. B

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

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

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