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

Spin Wave Instability of Itinerant Ferromagnet

We show variationally that instability of the ferromagnetic state in the Hubbard model is largely controlled by softening of a long-wavelength spin-wave excitation, except in the over-doped strong-coupling region where the individual-particle excitation becomes unstable first. A similar conclusion is drawn also for the double exchange ferromagnet. Generally the spin-wave instability may be regarded as a precursor of the metal-insulator transition.Comment: 11 pages, 8 figure

Folding of a donor–acceptor polyrotaxane by using noncovalent bonding interactions

Mechanically interlocked compounds, such as bistable catenanes and bistable rotaxanes, have been used to bring about actuation in nanoelectromechanical systems (NEMS) and molecular electronic devices (MEDs). The elaboration of the structural features of such rotaxanes into macromolecular materials might allow the utilization of molecular motion to impact their bulk properties. We report here the synthesis and characterization of polymers that contain π electron-donating 1,5-dioxynaphthalene (DNP) units encircled by cyclobis(paraquat-p-phenylene) (CBPQT4+), a π electron-accepting tetracationic cyclophane, synthesized by using the copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC). The polyrotaxanes adopt a well defined “folded” secondary structure by virtue of the judicious design of two DNP-containing monomers with different binding affinities for CBPQT4+. This efficient approach to the preparation of polyrotaxanes, taken alongside the initial investigations of their chemical properties, sets the stage for the preparation of a previously undescribed class of macromolecular architectures

Dispersion of Ordered Stripe Phases in the Cuprates

A phase separation model is presented for the stripe phase of the cuprates, which allows the doping dependence of the photoemission spectra to be calculated. The idealized limit of a well-ordered array of magnetic and charged stripes is analyzed, including effects of long-range Coulomb repulsion. Remarkably, down to the limit of two-cell wide stripes, the dispersion can be interpreted as essentially a superposition of the two end-phase dispersions, with superposed minigaps associated with the lattice periodicity. The largest minigap falls near the Fermi level; it can be enhanced by proximity to a (bulk) Van Hove singularity. The calculated spectra are dominated by two features -- this charge stripe minigap plus the magnetic stripe Hubbard gap. There is a strong correlation between these two features and the experimental photoemission results of a two-peak dispersion in La$_{2-x}$Sr$_x$CuO$_4$, and the peak-dip-hump spectra in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The differences are suggestive of the role of increasing stripe fluctuations. The 1/8 anomaly is associated with a quantum critical point, here expressed as a percolation-like crossover. A model is proposed for the limiting minority magnetic phase as an isolated two-leg ladder.Comment: 24 pages, 26 PS figure

Variational Monte Carlo Study of Spin-Gapped Normal State and BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model

We study properties of normal, superconducting (SC) and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable to induce a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength $|U|/t$ increases, a first-order spin-gap transition arises at $|U_{\rm c}|\sim W$ ($W$: band width) from a Fermi liquid to a spin-gapped state, which is conductive through hopping of doublons. In the SC state, we confirm by analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at around |U_{\ma{co}}|\sim |U_{\rm c}| from a BCS type to a Bose-Einstein condensation (BEC) type, as $|U|/t$ increases. For |U|<|U_{\ma{co}}|, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit behavior of $\sim \exp(-t/|U|)$, as expected from the BCS theory. For |U|>|U_{\ma{co}}|, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as $\sim t^2/|U|\propto T_{\rm c}$, as expected in a bosonic scheme. In this regime, the SC transition is induced by a gain in kinetic energy, in contrast with the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.Comment: 14 pages, 22 figures, submitted to Journal of the Physical Society of Japa

The Association Between IGF-1 Levels and the Histologic Severity of Nonalcoholic Fatty Liver Disease

Objectives: The mechanisms responsible for the development of nonalcoholic fatty liver disease (NAFLD) and progression to nonalcoholic steatohepatitis (NASH) are incompletely understood. Growing evidence suggests that growth hormone (GH) and insulin-like growth factor-1 (IGF-1) may have roles in the development and progression of NAFLD. We hypothesized that lower serum IGF-1 levels would be associated with increased liver fat accumulation, inflammation, and fibrosis in a group of meticulously phenotyped obese subjects with liver biopsies. Methods: A retrospective, cross-sectional study was performed at Massachusetts General Hospital, Boston, MA, USA and St. Mary's Hospital, Richmond, VA, USA. Liver biopsies were performed in 142 subjects during NAFLD work-up or bariatric surgery and were graded by a single, blinded pathologist. Main outcome measures included liver histology and serum IGF-1. Results: Mean age was 52±10 years and body mass index (BMI) was 43±9 kg/m2. Mean serum IGF-1 was lower in subjects with lobular inflammation (112±47 vs. 136±57 ng/ml, P=0.01), hepatocyte ballooning (115±48 vs. 135±57 ng/ml, P=0.05), higher fibrosis stage (stage 2–4 vs. 0–1; 96±40 vs. 125±51 ng/ml, P=0.005), and NASH (109±45 vs. 136±57 ng/ml, P=0.002). All results remained significant after controlling for age, BMI, and a diagnosis of diabetes, and all but hepatocyte ballooning (trend, P=0.06) remained significant after excluding individuals with cirrhosis. Steatosis was not significantly associated with mean serum IGF-1 levels. Conclusions: Low serum IGF-1 levels are associated with increased histologic severity of NAFLD when rigorously controlled for age, BMI, the presence of diabetes, and after the exclusion of subjects with cirrhosis. Further investigation is warranted to determine the differential effects of GH and IGF-1 on the development and progression of NAFLD, which could further elucidate pathophysiology and identify therapeutic targets

Evolution of Susceptibility to Ingested Double-Stranded RNAs in Caenorhabditis Nematodes

International audienceBACKGROUND: The nematode Caenorhabditis elegans is able to take up external double-stranded RNAs (dsRNAs) and mount an RNA interference response, leading to the inactivation of specific gene expression. The uptake of ingested dsRNAs into intestinal cells has been shown to require the SID-2 transmembrane protein in C. elegans. By contrast, C. briggsae was shown to be naturally insensitive to ingested dsRNAs, yet could be rendered sensitive by transgenesis with the C. elegans sid-2 gene. Here we aimed to elucidate the evolution of the susceptibility to external RNAi in the Caenorhabditis genus. PRINCIPAL FINDINGS: We study the sensitivity of many new species of Caenorhabditis to ingested dsRNAs matching a conserved actin gene sequence from the nematode Oscheius tipulae. We find ample variation in the Caenorhabditis genus in the ability to mount an RNAi response. We map this sensitivity onto a phylogenetic tree, and show that sensitivity or insensitivity have evolved convergently several times. We uncover several evolutionary losses in sensitivity, which may have occurred through distinct mechanisms. We could render C. remanei and C. briggsae sensitive to ingested dsRNAs by transgenesis of the Cel-sid-2 gene. We thus provide tools for RNA interference studies in these species. We also show that transgenesis by injection is possible in many Caenorhabditis species. CONCLUSIONS: The ability of animals to take up dsRNAs or to respond to them by gene inactivation is under rapid evolution in the Caenorhabditis genus. This study provides a framework and tools to use RNA interference and transgenesis in various Caenorhabditis species for further comparative and evolutionary studies

Bias and Evolution of the Mutationally Accessible Phenotypic Space in a Developmental System

Genetic and developmental architecture may bias the mutationally available phenotypic spectrum. Although such asymmetries in the introduction of variation may influence possible evolutionary trajectories, we lack quantitative characterization of biases in mutationally inducible phenotypic variation, their genotype-dependence, and their underlying molecular and developmental causes. Here we quantify the mutationally accessible phenotypic spectrum of the vulval developmental system using mutation accumulation (MA) lines derived from four wild isolates of the nematodes Caenorhabditis elegans and C. briggsae. The results confirm that on average, spontaneous mutations degrade developmental precision, with MA lines showing a low, yet consistently increased, proportion of developmental defects and variants. This result indicates strong purifying selection acting to maintain an invariant vulval phenotype. Both developmental system and genotype significantly bias the spectrum of mutationally inducible phenotypic variants. First, irrespective of genotype, there is a developmental bias, such that certain phenotypic variants are commonly induced by MA, while others are very rarely or never induced. Second, we found that both the degree and spectrum of mutationally accessible phenotypic variation are genotype-dependent. Overall, C. briggsae MA lines exhibited a two-fold higher decline in precision than the C. elegans MA lines. Moreover, the propensity to generate specific developmental variants depended on the genetic background. We show that such genotype-specific developmental biases are likely due to cryptic quantitative variation in activities of underlying molecular cascades. This analysis allowed us to identify the mutationally most sensitive elements of the vulval developmental system, which may indicate axes of potential evolutionary variation. Consistent with this scenario, we found that evolutionary trends in the vulval system concern the phenotypic characters that are most easily affected by mutation. This study provides an empirical assessment of developmental bias and the evolution of mutationally accessible phenotypes and supports the notion that such bias may influence the directions of evolutionary change