Entanglement in doped Resonating Valence Bond states

We investigate the entanglement properties of resonating valence bond states on a two dimensional lattice in the presence of dopants that remove electrons from the lattice creating “holes”. The movement of the holes generated by the Hubbard Hamiltonian in the regime of strong Coloumb repulsion in this setting could be responsible for the phenomenon of high temperature superconductivity as hypothesised by Anderson in Science {\bf 235}, 1196, (1987). We argue that there is a particular density of dopants (holes) where the entanglement contained in the lattice attains its maximal value for the nearest-neighbour RVB liquid state.