Non-Fermi liquid behavior in multi-orbital Anderson impurity models and possible relevance for strongly correlated lattice models

Contents Introduction 1 1 Dynamical mean field theory and impurity models 9 A Fermi liquid theory for the Anderson model 127 B Matrix elements for the three-orbital model 133 Bibliography 137 Acknowledgments 143 Introduction Soon after the discovery of high T c in cuprates, it was observed that some of their peculiar non-Fermi liquid properties could be explained phenomenologically by assuming a singular frequency (but not momentum) dependence of the electron self-energy, which was named as marginal-Fermi liquid behavior[1]. This observation stimulated a lot of activity in single-impurity models showing non-Fermi liquid behavior [2–5], which are the simplest cases where a singular frequency dependence may show up. Meanwhile non-Fermi liquid behavior started to be observed in uranium and cerium heavy-fermion compounds [6], which also admitted simple explanations through exotic single-impurity models [6] or phenomenological descriptions in terms of magnetic susceptibilities with anomalous frequency-but conventional momentum-dependence[7, 8]. All these theoretical attempts assumed, more or less implicitly, that a single-impurity behavior had chance to survive even in a translationally invariant system. This assumption is however not easy to justify theoretically. For instance, in the case of heavy-fermion compounds, one rather expects that, once the density of impurities is increased, the effects of the single-impurity singular behavior should be smoothened[9] and the non-Fermi liquid character lost. Even more difficult it is to relate the single-impurity behavior to the physics of cuprates, where the strength of the hybridization between the strongly correlated copper d-orbitals and the oxygen p-orbitals is comparable to the charge transfer gap. For these reasons and especially in the case of high T c superconductors, the original interest towards anomalous single-impurity models lessened rapidly. Actually a connection between lattice models and impurity models was just near to come and what was lacking in the earlier approaches was indeed fixed by dynamical mean field theory (DMFT)[10–12], which improves ordinary Hartree-Fock theory by treating exactly temporal fluctuations while considering spatial fluctuations within mean-field. This theory provided a rigorous frame-2 Introduction work in which a lattice model is mapped onto an Anderson impurity model (AIM) subject to a self-consistency condition which relates the impurity Green's function to the hybridization function with the conduction bath. The quasiparticle bandwidth of the lattice model transforms into the Kondo temperature T K of the AIM. As in the case of classical mean-field theory, DMFT is exact only for infinite lattice connec-tivity, which is its main limitation. In finite …