# The Split and Approximate Split Property in 2D Systems: Stability and Absence of Superselection Sectors

@article{Naaijkens2022TheSA, title={The Split and Approximate Split Property in 2D Systems: Stability and Absence of Superselection Sectors}, author={Pieter Naaijkens and Yoshiko Ogata}, journal={Communications in Mathematical Physics}, year={2022} }

The split property of a pure state for a certain cut of a quantum spin system can be understood as the entanglement between the two subsystems being weak. From this point of view, we may say that if it is not possible to transform a state $$\omega $$
ω
via sufficiently local automorphisms (in a sense that we will make precise) into a state satisfying the split property, then the state $$\omega $$
ω
has a long-range entanglement. It is well known that in 1D, gapped ground states have the…

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