Chen-Hsin invertible-order code[1]
Description
A geometrically local commuting-projector code that realizes beyond-group-cohomology invertible topological phases in arbitrary dimensions. Instances of the code in 4D realize the 3D \(\mathbb{Z}_2\) gauge theory with fermionic charge and either bosonic (FcBl) or fermionic (FcFl) loop excitations at their boundaries [2,3]; see Ref. [4] for a different lattice-model formulation of the FcBl boundary code.
Encoding
Parents
- Qubit code
- Two-gauge theory code — Chen-Hsin invertible-order codes realize beyond-group-cohomology invertible topological phases of order two and four in arbitrary dimensions. These phases are described by invertible two-gauge theories [1; pg. 11].
Cousins
- Abelian topological code — Instances of the code in 4D realize the 3D \(\mathbb{Z}_2\) gauge theory with fermionic charge and either bosonic (FcBl) or fermionic (FcFl) loop excitations at their boundaries [2,3]; see Ref. [4] for a different lattice-model formulation of the FcBl boundary code.
- Symmetry-protected topological (SPT) code — Instances of the Chen-Hsin invertible-order code realize beyond-group-cohomology SPTs [1].
References
- [1]
- Y.-A. Chen and P.-S. Hsin, “Exactly solvable lattice Hamiltonians and gravitational anomalies”, SciPost Physics 14, (2023) arXiv:2110.14644 DOI
- [2]
- T. Johnson-Freyd, “(3+1)D topological orders with only a \(\mathbb{Z}_2\)-charged particle”, (2020) arXiv:2011.11165
- [3]
- L. Fidkowski, J. Haah, and M. B. Hastings, “Gravitational anomaly of (3+1) -dimensional Z2 toric code with fermionic charges and fermionic loop self-statistics”, Physical Review B 106, (2022) arXiv:2110.14654 DOI
- [4]
- L. Fidkowski, J. Haah, and M. B. Hastings, “Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase”, Physical Review B 101, (2020) arXiv:1912.05565 DOI
- [5]
- L. Fidkowski, J. Haah, and M. B. Hastings, “A QCA for every SPT”, (2024) arXiv:2407.07951
Page edit log
- Victor V. Albert (2024-06-07) — most recent
Cite as:
“Chen-Hsin invertible-order code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/invertible