A dimerized spin fluid in a one-dimensional electron system

The ground state of a one-dimensional Hubbard model with a bond-charge attraction W term at half-filling is investigated by the density matrix renormalization group method. It is confirmed that the spin gap will be closed at U>8W. But the long-range bond order wave survives even when the spin gap is closed. It indicates that the ground state is a novel dimerized spin fluid at U>8W. By a charge-spin transformation, it is shown that there should be a dimerized metallic phase at U<-8W. Furthermore, it is found that the Hubbard interaction U enhances initially the dimerization for a weak bond charge attraction W whereas it reduces monotonously the dimerization for a stronger bond charge attraction W.