  Symmetric mass generation is a novel mechanism to give gapless fermions a
mass gap by non-perturbative interactions without generating any fermion
bilinear condensation. The previous studies of symmetric mass generation have
been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free
fermion limit. In this work, we generalize the concept of symmetric mass
generation to Fermi liquid with a finite Fermi volume and discuss how to gap
out the Fermi surfaces by interactions without breaking the U(1) loop group
symmetry or developing topological orders. We provide examples of Fermi surface
symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when
several Fermi surfaces together cancel the Fermi surface anomaly. However, the
U(1) loop group symmetry in these cases is still restrictive enough to rule out
all possible fermion bilinear gapping terms, such that a non-perturbative
interaction mechanism is the only way to gap out the Fermi surfaces. This
symmetric Fermi surface reconstruction is in contrast to the conventional
symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our
model provides a pristine 1D lattice regularization for the (1+1)D U(1)
symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice
translation symmetry as an emergent U(1) symmetry at low energy. This opens up
the opportunity for efficient numerical simulations of chiral fermions in their
own dimensions without introducing mirror fermions under the domain wall
fermion construction.
