I know when we talk about Insulator, U(1)charge symmetry naturally exists.
But in this article:Quantum phase transitions of topological insulators without gap closing, the author claims that:
"The Chern insulator is not an SPT phase protected by U(1)charge symmetry. In fact, a Chern insulator (and the QHE) is neither topologically ordered (or long-ranged entangled) nor symmetry-protected. It is simply a chiral phase due to broken time-reversal symmetry".
In this question:Do Chern Insulators (QAHE) have topological order (long-range quantum entanglement)? , Professor Wen says that:
Chern Insulator has "invertible" topological order and long-range entanglement. Chern Insulator does not need any symmetry, although one usually assume Chern Insulator has an U(1) symmetry.
So how to understand two explanations? Thanks a lot.


I believe your confusion comes from conflicting definitions of LRE. Wen's answer here should hopefully clear things up.


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