Non-Abelian Hybrid Fracton Orders

TL;DR

This paper introduces lattice gauge theories for three-dimensional hybrid fracton orders that combine features of topological and fracton phases, including non-Abelian excitations and a tunable interpolation between different orders.

Contribution

It constructs solvable lattice models for hybrid fracton orders, revealing how their properties depend on the choice of a finite group and a normal subgroup, and explores their relation to symmetry gauging and condensation.

Findings

Hybrid fracton orders can host non-Abelian, immobile point-like excitations.

The models interpolate between conventional gauge theories and pure fracton orders.

Universal data of excitations relate directly to the choice of groups G and N.

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.