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I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features of topological order in fractional quantum Hall effect, such as fractional statistics, symmetry factionalization. So what is the meaning when people say "there is no topological order at finite temperature in 2+1D"? And what is the situation in 3+1D?

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there are recent studies on 3+1D topological order in this Ref: arxiv.org/abs/1404.7854. Using Modular SL(3,Z) generalized from Modular SL(2,Z) of 2D; and using Dijkgraaf-Witten lattice TQFT, and string-string braidings to characterize 3+1D topological order. –  Idear Jun 24 at 2:08
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Can we say that if the mass gap of the anyon fractional exicitations $\Delta$ are larger than the thermal energy $E_H=k_b T$ (temperature at $T$),

$$ \Delta >> E_H=k_b T $$

then we still can observe topological order at small but finite temperature.(?)

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