A planar diagram approach to the correlation problem

We transpose an idea of 't Hooft from its context of Yang and Mills' theory of strongly interacting quarks to that of strongly correlated electrons in transition metal oxides and show that a Hubbard model of N interacting electron species reduces, to leading orders in N, to a sum of almost planar diagrams. The resulting generating functional and integral equations are very similar to those of the FLEX approximation of Bickers and Scalapino. This adds the Hubbard model at large N to the list of solvable models of strongly correlated electrons. PACS Numbers: 71.27.+a 71.10.-w 71.10.FdComment: revtex, 5 pages, with 3 eps figure

Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling

We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a consistent description of one- and two-particle quantities, needed for the stability analysis, we impose equations of motion on the one- as well on the two-particle Green functions simultaneously and introduce approximations in their input, the completely irreducible two-particle vertex. Thereby we do not loose singularities caused by multiple two-particle scatterings. We find a complete set of stability criteria and show that each instability, singularity in a two-particle function, is connected with a symmetry-breaking order parameter, either of density type or anomalous. We explicitly study the Hubbard model at intermediate coupling and demonstrate that approximations with static vertices get unstable before a long-range order or a metal-insulator transition can be reached. We use the parquet approximation and turn it to a workable scheme with dynamical vertex corrections. We derive a qualitatively new theory with two-particle self-consistence, the complexity of which is comparable with FLEX-type approximations. We show that it is the simplest consistent and stable theory being able to describe qualitatively correctly quantum critical points and the transition from weak to strong coupling in correlated electron systems.Comment: REVTeX, 26 pages, 12 PS figure

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

The Superconducting Instabilities of the non half-filled Hubbard Model in Two Dimensions

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) we reduce successively the cutoff $\Lambda$ about the Fermi surface and follow the renormalization of the coupling $U$ as a function of three energy-momenta. We calculate the intrinsic scale $T_{co}$ where the renormalization group flow crosses over from the regime ($\Lambda > T_{co}$) where the electron-electron (e-e) and electron-hole (e-h) terms are equally important to the regime ($\Lambda < T_{co}$) where only the e-e term plays a role. In the low energy regime only the pairing interaction $V$ is marginally relevant, containing contributions from all renormalization group steps of the regime $\Lambda > T_{co}$. After diagonalization of $V_{\Lambda =T_{co}}$, we identify its most attractive eigenvalue $\lambda _{\min}$. At low filling, $\lambda _{\min}$ corresponds to the $B_2$ representation ($d_{xy}$ symmetry), while near half filling the strongest attraction occurs in the $B_1$ representation ($d_{x^2-y^2}$ symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. Using the form of pairing and the structure of the renormalization group equations in the low energy regime, we give our interpretation of ARPES experiments trying to determine the symmetry of the order parameter in the Bi2212 high-$T_{c}$ compound.Comment: 24 pages (RevTeX) + 11 figures (the tex file appeared incomplete

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

Fluctuation Exchange Analysis of Superconductivity in the Standard Three-Band CuO2 Model

The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study instabilities in the standard three-band model for CuO2 layers in the high-temperature superconductors. Both intra-orbital and near-neigbor Coulomb interactions are retained. The filling dependence of the d(x2-y2) transition temperature is studied in both the "hole-doped" and "electron-doped" regimes using parameters derived from constrained-occupancy density-functional theory for La2CuO4. The agreement with experiment on the overdoped hole side of the phase diagram is remarkably good, i.e., transitions emerge in the 40 K range with no free parameters. In addition the importance of the "orbital antiferromagnetic," or flux phase, charge density channel is emphasized for an understanding of the underdoped regime.Comment: REVTex and PostScript, 31 pages, 26 figures; to appear in Phys. Rev. B (1998); only revised EPS figures 3, 4, 6a, 6b, 6c, 7 and 8 to correct disappearance of some labels due to technical problem

In Vivo Metabolism of Topically Applied Benzo[a]pyrene-4,5-oxide in Neonatal Rat Skin

The metabolism of benzo[a]pyrene (BP)-4,5-oxide in the skin and liver of neonatal rats was studied after topical application of the arene oxide in vivo. The metabolism of BP-4,5-oxide was time-dependent and showed a 2-h maximum for BP-4,5-dihydrodiol formation in both skin and liver. Product formation was also dose-dependent. Inhibitors of epoxide hydrolase such as clotrimazole, 1,1,1,-trichloropropene oxide, and cyclohexene oxide largely abolished the formation of BP-4,5-dihydrodiol. The rapid biotransformation of arene oxides such as BP-4,5-oxide in the skin emphasizes the potential importance of epoxide hydrolase in the activation and inactivation of polycyclic aromatic hydrocarbons. Furthermore, the topically applied arene oxide also penetrated the skin and was rapidly metabolized in the liver as well