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The lesson defines topological order partly through the entanglement entropy of a region A with smooth boundary:
S
(
A
)
=
α
∣
∂
A
∣
−
γ
+
…
S(A) = \alpha|\partial A| - \gamma + \dots
S
(
A
)
=
α
∣
∂
A
∣
−
γ
+
…
. What distinguishes a topologically ordered phase from a trivial phase in terms of the universal constant
γ
\gamma
γ
?
A trivial phase has
γ
>
0
\gamma > 0
γ
>
0
, while topological order means
γ
=
0
\gamma = 0
γ
=
0
A trivial phase has
γ
=
0
\gamma = 0
γ
=
0
, while topological order means
γ
>
0
\gamma > 0
γ
>
0
Both trivial and topological phases have
γ
=
0
\gamma = 0
γ
=
0
γ
\gamma
γ
is always negative for any gapped phase
Check answer