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

Pseudogap Formation in the Symmetric Anderson Lattice Model

We present self-consistent calculations for the self-energy and magnetic susceptibility of the 2D and 3D symmetric Anderson lattice Hamiltonian, in the fluctuation exchange approximation. At high temperatures, strong f-electron scattering leads to broad quasiparticle spectral functions, a reduced quasiparticle band gap, and a metallic density of states. As the temperature is lowered, the spectral functions narrow and a pseudogap forms at the characteristic temperature $T_x$ at which the width of the quasiparticle spectral function at the gap edge is comparable to the renormalized activation energy. For $T << T_x$, the pseudogap is approximately equal to the hybridization gap in the bare band structure. The opening of the pseudogap is clearly apparent in both the spin susceptibility and the compressibility.Comment: RevTeX - 14 pages and 7 figures (available on request), NRL-JA-6690-94-002

Collective Spin Fluctuation Mode and Raman Scattering in Superconducting Cuprates

Although the low frequency electronic Raman response in the superconducting state of the cuprates can be largely understood in terms of a d-wave energy gap, a long standing problem has been an explanation for the spectra observed in the $A_{1g}$ polarization orientations. We present calculations which suggest that the peak position of the observed $A_{1g}$ spectra is due to a collective spin fluctuation mode.Comment: 4 pages, 5 eps figure

Transport properties of strongly correlated metals:a dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling are calculated. Dynamical mean-field theory, which maps the Hubbard model onto a single impurity Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a non-monotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value, hbar a/e^2 (where "a" is a lattice constant) associated with mean-free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.Comment: 19 pages, 9 eps figure

On Migdal's theorem and the pseudogap

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical molecular fields. The model describes quasiparticles coupled to spin or charge fluctuations, and is solved by a Monte Carlo sampling of the molecular field distributions. When the molecular field correlations are sufficiently weak, the corrections to the self-consistent Eliashberg theory do not bring about qualitative changes in the quasiparticle spectrum. But for a range of model parameters near the magnetic boundary, we find that Migdal's theorem does not apply and the quasiparticle spectrum is qualitatively different from its mean-field approximation, in that a pseudogap opens in the quasiparticle spectrum. An important feature of the magnetic pseudogap found in the present calculations is that it is strongly anisotropic. It vanishes anlong the diagonal of the Brillouin zone and is large near the zone boundary. In the case of ferromagnetic fluctuations, we also find a range of model parameters with qualitative changes in the quasiparticle spectral function not captured by the one-loop approximation, in that the quasiparticle peak splits into two. We provide intuitive arguments to explain the physical origin of the breakdown of Midgal's theoremComment: revised versio

TEXTURES IN SLOWLY ROTATING 3He-A

Nous étudions les textures de 3He-A dans un cylindre infiniment long en rotation lente et nous comparons les énergies libres de trois configurations différentes.I study textures of 3He-A a slowly rotating infinitely long cylinder and compare the free energies of three possible configurations