Symmetry-Enforced Fermi Surfaces

TL;DR

This paper identifies a specific symmetry in quantum lattice fermion models that guarantees the existence of Fermi surfaces, revealing a fundamental link between symmetry and gapless electronic states.

Contribution

It introduces a new symmetry-enforced mechanism for Fermi surfaces in lattice fermion models, expanding understanding of gaplessness due to symmetry constraints.

Findings

Symmetry-enforced Fermi surfaces always exist in models with the identified symmetry.

The symmetry group is related to the Onsager algebra and includes a subgroup of even functions.

Fermi surfaces typically have at least two noncontractible components.

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