Dynamical Cluster Approximation Employing FLEX as a Cluster Solver

We employ the Dynamical Cluster Approximation (DCA) in conjunction with the Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA is a technique to systematically restore the momentum conservation at the internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which classes of Feynman diagrams are summed over analytically using geometric series. The FLEX is used as a tool to investigate the complementarity of the DCA and the finite size lattice technique with periodic boundary conditions by comparing their results for the Hubbard model. We also study the microscopic theory underlying the DCA in terms of compact (skeletal) and non-compact diagrammatic contributions to the thermodynamic potential independent of a specific model. The significant advantages of the DCA implementation in momentum space suggests the development of the same formalism for the frequency space. However, we show that such a formalism for the Matsubara frequencies at finite temperatures leads to acausal results and is not viable. However, a real frequency approach is shown to be feasible.Comment: 15 pages, 24 figures. Submitted to Physical Review B as a Regular Articl

Coherent Transport through an interacting double quantum dot: Beyond sequential tunneling

Various causes for negative differential conductance in transport through an interacting double quantum dot are investigated. Particular focus is given to the interplay between the renormalization of the energy levels due to the coupling to the leads and the decoherence of the states. The calculations are performed within a basis of many-particle eigenstates and we consider the dynamics given by the von Neumann-equation taking into account also processes beyond sequential tunneling. A systematic comparison between the levels of approximation and also with different formalisms is performed. It is found that the current is qualitatively well described by sequential processes as long as the temperature is larger than the level broadening induced by the contacts.Comment: 11 pages, 5 figures included in tex

Toward a systematic 1/d expansion: Two particle properties

We present a procedure to calculate 1/d corrections to the two-particle properties around the infinite dimensional dynamical mean field limit. Our method is based on a modified version of the scheme of Ref. onlinecite{SchillerIngersent}}. To test our method we study the Hubbard model at half filling within the fluctuation exchange approximation (FLEX), a selfconsistent generalization of iterative perturbation theory. Apart from the inherent unstabilities of FLEX, our method is stable and results in causal solutions. We find that 1/d corrections to the local approximation are relatively small in the Hubbard model.Comment: 4 pages, 4 eps figures, REVTe

d-wave Superconductivity in the Hubbard Model

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with help of the Dynamical Cluster Approximation (DCA). To solve the effective cluster problem we employ an extended Non Crossing Approximation (NCA), which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solutions with off-diagonal long range order. The maximal $T_c\approx 150K$ occurs for a doping $\delta\approx 20$ and the doping dependence of the transition temperatures agrees well with the generic high-$T_c$ phase diagram.Comment: 5 pages, 5 figure

Relationships between Larval and Juvenile Abundance of Winter-Spawned Fishes in North Carolina, USA

We analyzed the relationships between the larval and juvenile abundances of selected estuarine-dependent fishes that spawn during the winter in continental shelf waters of the U.S. Atlantic coast. Six species were included in the analysis based on their ecological and economic importance and relative abundance in available surveys: spot Leiostomus xanthurus, pinfish Lagodon rhomboides, southern flounder Paralichthys lethostigma, summer flounder Paralichthys dentatus, Atlantic croaker Micropogonias undulatus, and Atlantic menhaden Brevoortia tyrannus. Cross-correlation analysis was used to examine the relationships between the larval and juvenile abundances within species. Tests of synchrony across species were used to find similarities in recruitment dynamics for species with similar winter shelf-spawning life-history strategies. Positive correlations were found between the larval and juvenile abundances for three of the six selected species (spot, pinfish, and southern flounder). These three species have similar geographic ranges that primarily lie south of Cape Hatteras. There were no significant correlations between the larval and juvenile abundances for the other three species (summer flounder, Atlantic croaker, and Atlantic menhaden); we suggest several factors that could account for the lack of a relationship. Synchrony was found among the three southern species within both the larval and juvenile abundance time series. These results provide support for using larval ingress measures as indices of abundance for these and other species with similar geographic ranges and winter shelf-spawning life-history strategies

Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions

We consider a disordered d--wave superconductor in two dimensions. Recently, we have shown in an exact calculation that for a lattice model with a Lorentzian distributed random chemical potential the quasiparticle density of states at the Fermi level is nonzero. As the exact result holds only for the special choice of the Lorentzian, we employ different methods to show that for a large class of distributions, including the Gaussian distribution, one can establish a nonzero lower bound for the Fermi level density of states. The fact that the tails of the distributions are unimportant in deriving the lower bound shows that the exact result obtained before is generic.Comment: 15 preprint pages, no figures, submitted to PR

Towards analytical approaches to the dynamical-cluster approximation

I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a cluster solver for the Hubbard model. Thermodynamic properties are found to be practically indistinguishable from those computed using the full self-consistent scheme in all cases where the non-interacting partial density of states is replaced by simplified analytic forms with matching 1st and 2nd moments. Green functions are also compared and found to be in close agreement, and the density of states computed using Pad\'{e} approximant analytic continuation shows that dynamical properties can also be approximated effectively. Extensions to two-particle properties and multiple bands are discussed. Simplified approaches to the dynamical cluster approximation should lead to new analytic solutions of the Hubbard and other models

Systematic and Causal Corrections to the Coherent Potential Approximation

The Dynamical Cluster Approximation (DCA) is modified to include disorder. The DCA incorporates non-local corrections to local approximations such as the Coherent Potential Approximation (CPA) by mapping the lattice problem with disorder, and in the thermodynamic limit, to a self-consistently embedded finite-sized cluster problem. It satisfies all of the characteristics of a successful cluster approximation. It is causal, preserves the point-group and translational symmetry of the original lattice, recovers the CPA when the cluster size equals one, and becomes exact as $N_c\to\infty$. We use the DCA to study the Anderson model with binary diagonal disorder. It restores sharp features and band tailing in the density of states which reflect correlations in the local environment of each site. While the DCA does not describe the localization transition, it does describe precursor effects of localization.Comment: 11 pages, LaTeX, and 11 PS figures, to appear in Phys. Rev. B. Revised version with typos corrected and references adde

Spectral functions in itinerant electron systems with geometrical frustration

The Hubbard model with geometrical frustration is investigated in a metallic phase close to half-filling. We calculate the single particle spectral function for the triangular lattice within dynamical cluster approximation, which is further combined with non-crossing approximation and fluctuation exchange approximation to treat the resulting cluster Anderson model. It is shown that frustration due to non-local correlations suppresses short-range antiferromagnetic fluctuations and thereby assists the formation of heavy quasi-particles near half-filling.Comment: 4 pages, 5 eps figure

Low energy properties of M-state tunneling systems in metals: New candidates for non-Fermi-liquid systems

We construct a generalized multiplicative renormalization group transformation to study the low energy dynamics of a heavy particle tunneling among $M$ different positions and interacting with $N_f$ independent conduction electron channels. Using a $1/N_f$-expansion we show that this M-level scales towards a fixed point equivalent to the $N_f$ channel $SU(M) \times SU(N_f)$ Coqblin-Schrieffer model. Solving numerically the scaling equations we find that a realistic M-level system scales close to this fixed point (FP) and its Kondo temperature is in the experimentally observable range $1-10 K$.Comment: 11 Latex pages, to appear in Phys. Rev. Lett, Figures available from the author by reques