Sorting topological stabilizer models in three dimensions

Abstract

The S-matrix invariant is known to be complete for translation invariant topological stabilizer models in two spatial dimensions, as such models are phase equivalent to some number of copies of toric code. In three dimensions, much less is understood about translation invariant topological stabilizer models due to the existence of fracton topological order. Here we introduce bulk commutation quantities inspired by the 2D S-matrix invariant that can be employed to coarsely sort 3D topological stabilizer models into qualitatively distinct types of phases: topological quantum field theories, foliated or fractal type-I models with rigid string operators, or type-II models with no string operators.

14+29 pages, 7+22 figures, 3+34 tables

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Cited by in corpus (39)

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• Fractonic Superfluids
• Topological Defect Networks for Fractons of all Types
• Single-shot error correction of three-dimensional homological product codes
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Fault-Tolerant Quantum Gates with Defects in Topological Stabiliser Codes
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Fractonic superfluids. (II). Condensing subdimensional particles
• Operator relaxation and the optimal depth of classical shadows
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Fracton physics of spatially extended excitations
• Type-II fractons from coupled spin chains and layers
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• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
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• Topological graph states and quantum error correction codes
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• Error-correcting codes for fermionic quantum simulation
• Fractonic topological phases from coupled wires
• Fractalizing quantum codes
• Topological defect network representations of fracton stabilizer codes
• Fracton-like phases from subsystem symmetries
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• No Strings Attached: Boundaries and Defects in the Cubic Code
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