Analytical wave function and reduced Hamiltonian for the weakly coupled two-dimensional Hubbard model.

Abstract

We introduce a many-body wave function that is shown to describe accurately the ground state of the positive-U, two-dimensional Hubbard model on finite lattices close to half-filling. The wave function is used to demonstrate the absence of a conventional BCS ground state and pairing instability. A simple reduced Hamiltonian describing transverse spin fluctuations is obtained as the fixed-point Hamiltonian in the limit U\ensuremath{\simeq}\ensuremath{\Delta}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{s}}$ where \ensuremath{\Delta}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{s}}$ is the single-particle energy-level spacing at the Fermi surface.