Physics of projected wavefunctions

Abstract

We present and discuss a variational approach to the one band Hubbard model in the limit of a large on-site Coulomb repulsion. The trial wavefunctions are the projected wavefunctions, generalized Gutzwiller wavefunctions. We discuss in detail the definition of these wavefunctions, the numerical methods used to evaluate them, their properties, and their physical relevance. Depending on the kind of parametrization used, the projected wavefunctions can describe a nearly localized Fermi liquid, an antiferromagnetically ordered state, or a quantum spin liquid. The physics of these three types of wavefunctions is described in detail. We discuss their relation to a proposed phase diagram of the two-dimensional Hubbard model and to results obtained by other approaches to the Hubbard model. The results obtained by numerical evaluation of the projected wavefunction are reviewed. The method used for the numerical evaluation, the variational Monte Carlo method, is described in detail. Finally we discuss the relation between a quantum spin liquid and the resonating valence bond state, which has been proposed, by P.W. Anderson, as a reference state for the Cu-O superconductors. In particular, we examine the question whether a quantum spin liquid is intrisically superconducting or not.