Theoretical Evidence for the Equivalence between the Ground States of the Strong-Coupling BCS Hamiltonian and the Antiferromagnetic Heisenberg Model

By explicitly computing wavefunction overlap via exact diagonalization, we show that, in the limit of strong coupling, the ground state of the Gutzwiller-projected BCS Hamiltonian (accompanied by proper particle-number projection) is identical to the exact ground state of the 2D antiferromagnetic Heisenberg model on the square lattice. This identity is adiabatically connected to a very high overlap between the ground states of the projected BCS Hamiltonian and the $t$-$J$ model at moderate doping.