Symmetry-Enforced Fermi Surfaces

We identify a symmetry that enforces every symmetric model to have a Fermi surface. These symmetry-enforced Fermi surfaces are realizations of a powerful form of symmetry-enforced gaplessness. The symmetry we construct exists in quantum lattice fermion models on a d-dimensional Bravais lattice, and is generated by the on-site U(1) fermion number symmetry and non-on-site Majorana translation symmetry. The resulting symmetry group is a noncompact Lie group closely related to the Onsager algebra. For a symmetry-enforced Fermi surface F, we show that this UV symmetry group always includes the subgroup of the ersatz Fermi liquid L_{F}U(1) symmetry group formed by even functions f(k)∈U(1) with k∈F. Furthermore, we comment on the topology of these symmetry-enforced Fermi surfaces, proving they generically exhibit at least two noncontractible components (i.e., open orbits).