Luttinger liquid phase in the Aubry-André Hubbard chain

We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.