Nature of ground states in one-dimensional electron-phonon Hubbard models at half filling

The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the (U, g(ph)) plane for the phonon-mediated interaction g(ph) and the Coulomb interaction U. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency omega(0). We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical U* approximate to g(ph)*, followed at larger U similar to g(ph) by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on U. For the Peierls-Hubbard model, the region of the (U, g(ph)) plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency omega(D) decreases. A power-law dependence g(ph) similar to U-2 eta is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term V is added to the Hubbard interaction.