  The Fermi surface symmetric mass generation (SMG) is an intrinsically
interaction-driven mechanism that opens an excitation gap on the Fermi surface
without invoking symmetry-breaking or topological order. We explore this
phenomenon within a bilayer square lattice model of spin-1/2 fermions, where
the system can be tuned from a metallic Fermi liquid phase to a
strongly-interacting SMG insulator phase by an inter-layer spin-spin
interaction. The SMG insulator preserves all symmetries and has no mean-field
interpretation at the single-particle level. It is characterized by zeros in
the fermion Green's function, which encapsulate the same Fermi volume in
momentum space as the original Fermi surface, a feature mandated by the
Luttinger theorem. Utilizing both numerical and field-theoretical methods, we
provide compelling evidence for these Green's function zeros across both strong
and weak coupling regimes of the SMG phase. Our findings highlight the
robustness of the zero Fermi surface, which offers promising avenues for
experimental identification of SMG insulators through spectroscopy experiments
despite potential spectral broadening from noise or dissipation.
