Non-Abelian Hybrid Fracton Orders

• URL: http://arxiv.org/abs/2106.03842v2
• Date: Sat, 11 Sep 2021 23:37:45 GMT
• Title: Non-Abelian Hybrid Fracton Orders
• Authors: Nathanan Tantivasadakarn, Wenjie Ji, Sagar Vijay
• Abstract summary: lattice gauge theories describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders. We construct solvable lattice models for these orders which interpolate between a conventional, three-dimensional $G$ gauge theory and a pure fracton order. We demonstrate that certain universal data of the topological excitations and their mobilities are directly related to the choice of $G$ and $N$.
• Score: 0.8250374560598496
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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