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arXiv · 2512.04150

Symmetry-Enforced Fermi Surfaces

Minho Luke Kim·Salvatore D. Pace·Shu-Heng Shao
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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).

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Minho Luke Kim, Salvatore D. Pace, Shu-Heng Shao. 2025-12-03. Symmetry-Enforced Fermi Surfaces. https://doi.org/10.1103/wpdt-4t1c

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