Non-Abelian Hybrid Fracton Orders

Abstract

We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a choice of an Abelian normal subgroup $N$, and a choice of foliation structure. These hybrid fracton orders -- examples of which were introduced in arXiv:2102.09555 -- can also host immobile, point-like excitations that are non-Abelian, and therefore give rise to a protected degeneracy. We construct solvable lattice models for these orders which interpolate between a conventional, three-dimensional $G$ gauge theory and a pure fracton order, by varying the choice of normal subgroup $N$. We demonstrate that certain universal data of the topological excitations and their mobilities are directly related to the choice of $G$ and $N$, and also present complementary perspectives on these orders: certain orders may be obtained by gauging a global symmetry which enriches a particular fracton order, by either fractionalizing on or permuting the excitations with restricted mobility, while certain hybrid orders can be obtained by condensing excitations in a stack of initially decoupled, two-dimensional topological orders.

17+11 pages, 4 figures, 7 tables. Added discussion on planons supported in multiple layers. Published version

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• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Classification and construction of interacting fractonic higher-order topological phases
• Fractionalization of subsystem symmetries in two dimensions
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
• No Strings Attached: Boundaries and Defects in the Cubic Code
• Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
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• There and Back Again: A Gauging Nexus between Topological and Fracton Phases