  It is widely believed that the spectral gap above the Fermi sea ground state
of lattice free fermions is stable against generic weak interactions. Quite
recently, Hastings presented a new interesting idea to prove the stability for
Majorana free fermions. He ingeniously used Majorana fermions so that the
unperturbed Hamiltonian of the free fermion part is mapped into a
frustration-free form. In this paper, we refine Hastings's argument, and give a
complete proof of the stability of the spectral gap above the Fermi sea ground
state against generic weak interactions for generic lattice free fermions.
