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 $(U,g_{rm ph})$ plane for the phonon-mediated interaction $g_{rm ph}$ 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^*approx g^*_{rm ph}$, followed at larger $Usim g_{rm ph}$ 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 $(U,g_{rm ph})$ 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 $g_{rm ph} sim U^{2eta}$ 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.

Role of electron-phonon interaction in a magnetically driven mechanism for superconductivity

We use the renormalization group method to examine the effect of phonon mediated interaction on d-wave superconductivity, as driven by spin fluctuations in a quasi-one-dimensional electron system. The influence of a tight-binding electron-phonon interaction on the spin-density-wave and d-wave superconducting instability lines is calculated for arbitrary temperature, phonon frequency and antinesting of the Fermi surface.The domain of electron-phonon coupling strength where spin-density-wave order becomes unstable against the formation of a bond-order-wave or Peierls state is determined at weak antinesting. We show the existence of a positive isotope effect for spin-density-wave and d-wave superconducting critical temperatures which scales with the antinesting distance from quantum critical point where the two instabilities merge. We single out a low phonon frequency zone where the bond-oder-wave ordering gives rise to triplet f-wave superconductivity under nesting alteration, with both orderings displaying a negative isotope effect. We also study the electron-phonon strengthening of spin fluctuations at the origin of extended quantum criticality in the metallic phase above superconductivity. The impact of our results on quasi-one-dimensional organic conductors like the Bechgaard salts where a Peierls distortion is absent and superconductivity emerges near a spin-density-wave state under pressure is emphasized.