Haah codes on general three manifolds

Abstract

Haah codes represent a singularly interesting gapped Hamiltonian schema that has resisted a natural generalization, although recent work shows that the closely related type I fracton models are more commonplace. These type I siblings of Haah codes are better understood, and a generalized topological quantum field theory framework has been proposed. Following the same conceptual framework, we outline a program to generalize Haah codes to all 3-manifolds using Hastings' LR stabilizer codes for finite groups.

arXiv commentTo appear in Ann. Physics

References in corpus (4)

• Local stabilizer codes in three dimensions without string logical operators
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Commuting Pauli Hamiltonians as maps between free modules
• Algebraic Methods for Quantum Codes on Lattices

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• Fractonic Superfluids
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• Twisted foliated fracton phases
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• Fractonic superfluids. (II). Condensing subdimensional particles
• Fracton physics of spatially extended excitations
• Generating Lattice Non-invertible Symmetries
• Boson-fermion duality with subsystem symmetry
• Symmetric higher rank topological phases on generic graphs
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation