Projected BCS theory for high-temperature superconductivity

At the core of the problem of high-temperature superconductivity lies the relationship between strong correlation and superconductivity. One of the most exciting prospects on their relationship is that strong correlation is the very source of high-temperature superconductivity. To investigate the validity of this prospect, we perform a variational analysis of the BCS model Hamiltonian projected onto the constrained Hilbert space with infinitely strong correlation, or no double occupancy. This is also known as the Gutzwiller projection. For convenience, let us call such an analysis the projected BCS theory. By computing the overlap between the exact ground states of the projected BCS theory and those of the t-J model via exact diagonalization, here, we show that the projected BCS theory provides excellent variational states for the ground states of the t-J model in the entire range of hole concentration including both half filling and finite doping. It is emphasized that the resonating valence bond (RVB) state, i.e., the projected BCS wave function is closely related to the ground state of the projected BCS theory, while quite different at low doping. What makes the difference is whether the projection is applied to the ground state of the Hamiltonian or the Hamiltonian itself.