\(G\)-enriched Walker-Wang model code[1]
Also known as Williamson-Wang model code.
Description
A 3D topological code defined by a unitary \(G\)-crossed braided fusion category \( \mathcal{C} \) [2,3], where \(G\) is a finite group. The model realizes TQFTs that include two-gauge theories, those behind Walker-Wang models, as well as the Kashaev TQFT [4,5]. It has been generalized to include domain walls [6].
Parents
- Category-based quantum code
- Commuting-projector Hamiltonian code — \(G\)-enriched Walker-Wang model codewords form ground-state subspaces of frustration-free commuting projector Hamiltonians.
- Frustration-free Hamiltonian code — \(G\)-enriched Walker-Wang model codewords form ground-state subspaces of frustration-free commuting projector Hamiltonians.
- Topological code — \(G\)-enriched Walker-Wang models realize 3D topological phases based on unitary \(G\)-crossed braided fusion categories.
Child
- Walker-Wang model code — \(G\)-enriched Walker-Wang models reduce to Walker-Wang models for trivial \(G\) [1].
Cousin
- Two-gauge theory code — \(G\)-enriched Walker-Wang models realize 3D two-gauge theories [1].
References
- [1]
- D. J. Williamson and Z. Wang, “Hamiltonian models for topological phases of matter in three spatial dimensions”, Annals of Physics 377, 311 (2017) arXiv:1606.07144 DOI
- [2]
- M. Barkeshli et al., “Symmetry fractionalization, defects, and gauging of topological phases”, Physical Review B 100, (2019) arXiv:1410.4540 DOI
- [3]
- S. X. Cui, “Four dimensional topological quantum field theories from \(G\)-crossed braided categories”, Quantum Topology 10, 593 (2019) arXiv:1610.07628 DOI
- [4]
- R. Kashaev, “A simple model of 4d-TQFT”, (2014) arXiv:1405.5763
- [5]
- R. Kashaev, “On realizations of Pachner moves in 4D”, (2015) arXiv:1504.01979
- [6]
- D. Bulmash and M. Barkeshli, “Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions”, Physical Review Research 2, (2020) arXiv:2003.11553 DOI
Page edit log
- Victor V. Albert (2024-06-20) — most recent
Cite as:
“\(G\)-enriched Walker-Wang model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/enriched_walker_wang