Possibility of a metallic phase in the charge-density-wave-spin-density-wave crossover region in the one-dimensional Hubbard-Holstein model at half filling

The Hubbard-Holstein model is studied at half filling in one dimension using a variational method based on the variable-displacement Lang-Firsov canonical transformation and the exact solution to the Hubbard model due to Lieb and Wu. It is usually believed that the system undergoes a direct insulator-to-insulator transition from charge-density wave (CDW) to spin-density wave (SDW) with the increase of the on-site Coulomb repulsion U for a given strength of the electron-phonon coupling. Here, we show indications that, at least in the antiadiabatic region, an intervening metallic state may exist in the crossover region of the CDW-SDW transition.