Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases

Abstract

We introduce hybrid fracton orders: three-dimensional gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders. Hybrid fracton orders host both (i) mobile topological quasiparticles and loop excitations, as well as (ii) point-like topological excitations with restricted mobility, with non-trivial fusion rules and mutual braiding statistics between the two sets of excitations. Furthermore, hybrid fracton phases can realize either conventional three-dimensional topological orders or fracton orders after undergoing a phase transition driven by the condensation of certain gapped excitations. Therefore, they serve as parent orders for both long-range-entangled quantum liquid and non-liquid phases. We study the detailed properties of hybrid fracton phases through exactly solvable models in which the resulting orders hybridize a three-dimensional ${\mathbb{Z}}_2$ topological order with (i) the X-Cube fracton order, or (ii) Haah's code. The hybrid orders presented here can also be understood as the deconfined phase of a gauge theory whose gauge group is given by an Abelian global symmetry $G$ and subsystem symmetries of a normal subgroup $N$ along lower-dimensional sub-regions. A further generalization of this construction to non-Abelian gauge groups is presented in arXiv:2106.03842.

19+10 pages, 17 figures, 5 tables. Published version

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• Subdimensional criticality: condensation of lineons and planons in the X-cube model
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• Towards Non-Invertible Anomalies from Generalized Ising Models
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Classification and construction of interacting fractonic higher-order topological phases
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• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
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• Topological Dipole Insulator
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