Optical spectral weights and the physics of correlated electron systems

Summary form only given. The essence of the "strong correlation" problem is that interactions reduce the ability of electrons to move in a solid. Optical conductivity probes, over a wide range of time scales, the ability of electrons to move, and is therefore a key probe of correlated electron physics. One simple and robust feature of the conductivity is the "spectral weight," the integral of the conductivity over some frequency range. I present theoretical results for the spectral weights of models relevant to correlated electron physics, and by comparing them to data show how they may be used to elucidate the physics of two systems of current interest: the high temperature superconductors and the "colossal" magnetoresistance manganites. I then turn to more detailed features of the conductivity, showing how analysis of the real and imaginary parts of the conductivity may be interpreted in terms of a scattering rate and mass enhancement. This analysis, in combination with the spectral weight analysis, is used to show that in the colossal magnetoresistance materials the important interaction is an unusually strong electron-phonon coupling. It is further argued that this analysis is inappropriate for the high temperature superconductors and perhaps for the three dimensional ferromagnet SrRuO/sub 3/, indicating the existence of a fundamentally non Fermi liquid state in these systems.