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I know IQHE is a example having "invertible" topological order from Professor Wen's definition. And Topological Insulators is SRE because of necessary of underlying symmetry protection. After that, the Chern Insulator (QAHE) needs a underlying TRS-broken not a TRS protection like IQHE. Except the external magnetic field, it is almost as same as IQHE. Is it also a example having long-range quantum entanglement? More precisely speaking, what topological order does it have? Also "invertible" topological order?

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Chern Insulator = QAHE = IQHE. Chern Insulator has "invertible" topological order and long-range entanglement as defined in https://arxiv.org/abs/1004.3835 . Chern Insulator does not need any symmetry, although one usually assume Chern Insulator has an U(1) symmetry.

Q: what topological order does IQHE have?

A: An "invertible" topological order characterized by a gravitational Chern-Simons term.

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  • $\begingroup$ Really the case. Thanks, Prof. Wen. $\endgroup$ – yalei lu Mar 16 '19 at 4:48

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