Classification of three-dimensional gapped phases including fractons · revision history
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Accepted · first revision · record
- Title
- Classification of three-dimensional gapped phases including fractons
- Plain
- In three dimensions some gapped phases have excitations that cannot move freely (fractons), and no complete list of 3D gapped phases that includes them exists.
- Precise
- Classify gapped phases of 3D local bosonic and fermionic lattice Hamiltonians up to adiabatic deformation and stacking with decoupled 2D gapped layers (foliation equivalence), including fracton phases whose ground-state degeneracy grows with system size. Existing classifications of 3D topological orders (Lan, Kong, Wen 2018; Lan, Wen 2019) assume no fracton excitations. An answer is a set of invariants that distinguish all phases, including a criterion separating foliated from non-foliated fracton orders.
- Settled by
- A set of invariants for 3D gapped lattice phases shown to distinguish all known fracton models and to be complete within a stated framework.
- Kind
- well-posed
- Answer type
- classification
- References
- (empty)
- Literature status
- partially-resolved
- Status note
- 3D bosonic topological orders with bosonic (Lan, Kong, Wen 2018) and fermionic (Lan, Wen 2019) pointlike excitations were classified for non-fracton orders; a classification including fracton orders is incomplete as of 2026.
- Posed since
- (empty)