Quantum-entanglement entropy and double occupancy in a 1-D Holstein-Hubbard model at half-filling

The nature of the cross-over region of the spin-density wave and the charge-density wave phases of the onedimensional Holstein-Hubbard model is examined at half filling. The vibrational modes have been removed by applying a set of canonical transformations followed by an averaging with a many-phonon state. The resulting effective Hubbard Hamiltonian is dealt exactly by using the method of Bethe-Ansatz to get the ground state energy of the system. The quantum entanglement entropy and double occupancy are calculated at the boundary of the spin and charge density wave phases to confirm the existence of an intervening metallic phase.