Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions

We present numerical evidence for a paradigm in one-dimensional interacting fermion systems, whose phenomenology has traits of both Luttinger liquids and Fermi liquids. This state, dubbed a quasi-Fermi liquid, possesses a discontinuity in its fermion occupation number at the Fermi momentum. The excitation spectrum presents particlelike quasiparticles and absence of holelike quasiparticles, giving rise instead to edge singularities. Such a state is realized in a one-dimensional spinless fermion lattice Hamiltonian by fine-tuning the interactions to a regime where they become irrelevant in the renormalization group sense. We show, using uniform infinite matrix products states and finite-entanglement scaling analysis, that the system ground state is characterized by a Luttinger parameter $K = 1$ and a discontinuous jump in the fermion occupation number. We support the characterization with calculations of the spectral function that show a particle-hole asymmetry reflected in the existence of well-defined Landau quasiparticles above the Fermi level and edge singularities without the associated quasiparticles below. These results indicate that the quasi-Fermi liquid paradigm can be realized beyond the low-energy perturbative realm.