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[en] The quantum phase transition from a spin-density wave phase to a charge-density wave phase is studied within the framework of the one-dimensional Holstein-Hubbard model. The phonons are first eliminated by using a variational phonon state and the effective electronic Hamiltonian is then exactly solved using the Bethe ansatz technique to get the ground state energy. The entanglement entropy is finally calculated to show the possibility of existence of an intervening metallic phase at the cross-over region of the spin-density and charge-density wave phases in the thermodynamic limit at half-filling.