Sixteen-Fold Way for Fermionic Topological Orders

• URL: http://arxiv.org/abs/2606.28682v1
• Date: Sat, 27 Jun 2026 01:48:39 GMT
• Title: Sixteen-Fold Way for Fermionic Topological Orders
• Abstract summary: We identify a new family of (2)D fermionic topological orders, forming a fermionic analogue of Kitaev's sixteen-fold way.<n>The simplest new example is an Abelian fermionic topological order containing a single $mathbbZ$ Abelian anyon of spin 1/8.
• Score: 0.643682905866995
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fermionic topological orders can host 't Hooft anomalies with no bosonic counterpart. We identify a new sixteen-fold family of (2+1)D fermionic topological orders, forming a fermionic analogue of Kitaev's sixteen-fold way. This family is distinguished by the mod 16 't Hooft anomaly of a $\mathbb{Z}_2$ one-form symmetry, generated in each theory by a single nontrivial $\mathbb{Z}_2$ anyon. This intrinsically fermionic anomaly permits anyon spins that are forbidden in bosonic phases; the simplest new example is an Abelian fermionic topological order containing a single $\mathbb{Z}_2$ Abelian anyon of spin 1/8. Each theory can be realized as the gapped boundary of a (3+1)D fermionic symmetry-protected topological (SPT) phase protected by the $\mathbb{Z}_2$ one-form symmetry, which acquires a $\mathbb{Z}_{16}$ classification once the spacetime spin structure is twisted by the one-form symmetry. We realize these phases microscopically via lattice models built from Walker-Wang models coupled to local fermions.

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