Fermi Surface Symmetric Mass Generation

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interaction effect without spontaneously generating any fermion bilinear condensation. So far, the discussion of symmetric mass generation has been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the notion of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to trivially gap out the Fermi surface(s) by interactions without breaking the protecting U(1) loop group symmetry. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems without 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-trivial interaction mechanism is the only way out. As a side product, our (1+1)D model provides a lattice regularization for the 3-4-5-0 chiral Fermi model by utilizing lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for more efficient numerical simulations of chiral fermions at low dimensions.