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Paper 1
Topological Order with a Twist: Ising Anyons from an Abelian Model
H. Bombin
- Year
- 2010
- Journal
- arXiv preprint
- DOI
- arXiv:1004.1838
- arXiv
- 1004.1838
Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons. These ideas can also be applied in the context of topological codes.
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On Symmetry-Compatible Superselection Structures for Product States in 2D Quantum Spin Systems
Matthew Corbelli
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.23790
- arXiv
- 2510.23790
We study superselection sectors in two-dimensional quantum spin systems with an on-site action of a compact abelian group $G$. Naaijkens and Ogata (2022) arXiv:2102.07707 showed that for states quasi-equivalent to a product state, the superselection structure is trivial, reflecting the absence of long-range entanglement. We consider a symmetry-compatible refinement of this setting, in which both the superselection criterion and the notion of equivalence between representations are required to respect the $G$-action. Under this stricter notion of equivalence, the sector structure for a $G$-equivariant product representation becomes nontrivial: the $G$-equivariant superselection sectors are classified by elements of the Pontryagin dual $\widehat{G}$. This shows that even in phases without long-range entanglement, imposing symmetry compatibility can lead to nontrivial sector structure.
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