  We present a class of one-dimensional generic spinless fermion lattice
Hamiltonians that express quasi-Fermi liquid physics, manifesting both
Luttinger and Fermi liquid features due to solely irrelevant interactions.
Using infinite matrix product state techniques, we unveil its universal
structure by calculating static and dynamic responses. Key features include a
finite discontinuity in the momentum distribution at the Fermi level, despite
power-law singularities in the spectral function protected by particle-hole
symmetry. Away from half-filling Landau quasiparticles emerge. Charge dynamics
show either high-energy bound states or concentration of spectral weight within
the continuum for attractive or repulsive interactions, respectively. These
universal features are realized across multiple models and energy scales thus
reifying the quasi-Fermi liquid as a unique paradigm for one-dimensional
fermions.
