Theory of the marginal-Fermi-liquid spectrum and pairing in a local copper oxide model

We solve for the properties of an impurity model abstracted from a model of copper oxide superconductors. At mixed valence, provided that Friedel's screening condition is satisfied, the marginal-Fermi-liquid spectrum is obtained for the spin and charge susceptibilities. The frequency dependence of the self-energies is {Σ}({ω}){~}{ω} ln{ω}+i{ω}. This critical point is surrounded by two different Fermi-liquid phases. A simplified two-impurity version of this model is also addressed, and presents similar features, including a logarithmic divergence for coherent pair susceptibility.