  Recently a new phenomenological Hamiltonian was proposed to describe the
superconducting cuprates in which correlations and on-site Coulomb repulsion
are introduced by partial Gutzwiller projection. This Gossamer Hamiltonian has
an exact ground state and differs from the t-J and Hubbard Hamiltonians in
possessing a powerful attractive interaction among electrons responsible for
Cooper pairing in the d-wave channel. It is a faithful description for a
superconductor with strong on-site electronic repulsion. The superconducting
tunneling gap remains intact and despite on-site repulsion. Near half-filling
the Gossamer superconductor with strong repulsion has suppressed photoemission
intensities and superfluid density, is unstable toward an antiferromagnetic
insulator and possesses an incipient Mott-Hubbard gap. The Gossamer technique
can be applied to metallic ground states thus possibly serving as an apt
description of strongly correlated metals. Such a Gossamer metallic phase, just
as the Gossamer superconducting one, becomes arbitrarily hard to differentiate
from an insulator as one turns the Coulomb correlations up near half-filling.
Both the metallic and superconducting states undergo a quantum phase transition
to an antiferromagnetic insulator as one increases the on-site Coulomb
repulsion. In the Gossamer model we reach the critical point at half-filling by
fully projecting out the double occupancy. Such a critical point might be the
Anderson Resonating Valence bond state.
