Correlated ground state of the Hubbard model

The variational many-body approach or, more generally, the method of correlated basis functions initiated for a quantitative analysis of strongly interacting quantum fluids may be adapted with minor modifications for exploring the properties of lattice models. This is demonstrated by performing an explicit analysis of the paramagnetic ground state of the Hubbard model. In a first step of the approximation scheme we represent the correlated state by a spin-dependent wave function of Jastrow-type. We analyze in detail the associated density-matrix elements and set up the corresponding Fermi hypernetted-chain equations which determine the irreducible constituents of these quantities. The solutions are discussed and constructed by iteration in terms of cluster approximants. Specializing the input data and the formal results provides a Fermi hypernetted-chain analysis of the correlations induced by a ground state wave function of the Gutzwiller form.