One Hole in a High Temperature Superconductor: Fermi Liquid?

We present a microscopic model of the high temperature superconductors which provides evidence for non-Fermi liquid behaviour. Starting from the Anderson Lattice model, we derive a three-band model of a CuO2 plane. We show that the popular t-J model is a subset of our model under certain assumptions which we show to be unphysical. We study the three-band model on the CuO chain. Using two exact solutions of the model to provide trial variational states, and comparing these with an exact finite system numerical calculation, we demonstrate that the spin degeneracy is lifted by the hole motion alone. This provides Heisenberg spin correlations for a physical choice of parameters, and the system is found to be a Luttinger liquid. In two dimensions we numerically solve a series of systems which limit to the CuO2 plane. We predict that the CuO2 planes will exhibit a highly quantum ground state dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. These predictions are contrary to those of the t-J model, where the hole motion alone predicts huge spin degeneracy for the linear chain, and Nagaoka ferromagnetism for the planar system.