Symmetry-Enforced Fermi Surfaces

Abstract

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 $\mathcal{F}$, we show that this UV symmetry group always includes the subgroup of the ersatz Fermi liquid L${}_{\mathcal{F}}$U(1) symmetry group formed by even functions $f(\mathbf{k})\in \mathrm{U}(1)$ with $\mathbf{k}\in \mathcal{F}$. 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).

7 pages plus appendices, 1 figure