Universal Luttinger liquid/Fermi liquid mixing in fermionic quantum fluids

One-dimensional, interacting fermions are described by Luttinger liquid theory, with collective excitations as opposed to quasiparticles characteristic of Fermi liquids. We demonstrate that there exist regimes where this picture is incomplete. Resorting to a tensor-network study of a generic class of locally-interacting, spinless fermion models, we show that the universal physics is described instead by a "quasi-Fermi liquid" that realizes both Fermi and Luttinger liquids behavior concurrently, with well-defined quasiparticles and power-law excitations. Key features include a Fermi-level finite discontinuity in the momentum distribution, despite power-law singularities in the spectral function. Away from half-filling Landau quasiparticles emerge. Charge dynamics show either high-energy bound states within the continuum. Our work suggests that the quasi-Fermi liquid restores Fermi-liquid physics in one dimension.