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We study the interplay between an on-site Hubbard repulsion and quasiperiodicpotential in one-dimensional fermion chains using the density matrixrenormalization group. We find that, at half-filling, the quasiperiodicpotential can destroy the Mott gap, leading to a metallic Luttinger liquidphase between the gapped Mott insulator at strong repulsion and localizedgapless Aubry- Andr\'e insulator at strong quasiperiodic potential. Away fromhalf-filing, the metallic phase of the interacting model persists to largercritical strengths of the potential than in the non-interacting case,suggesting interaction-stabilized delocalization at finite doping. Wecharacterize the Luttinger liquid through its charge and spin correlations,structure factors, and entanglement entropy.

Luttinger Liquid phase in the Aubry-Andr\'e Hubbard chain