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Haah codes on general three-manifolds. (English) Zbl 1432.81056

Summary: 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.

MSC:

81T45 Topological field theories in quantum mechanics
94B99 Theory of error-correcting codes and error-detecting codes
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