Take the tour ×  I know long-range entanglement is the essence
of nontrivial topological ordered states. (Trivial refers to
short range entangled and nontrivial refers to long range.) So,
entanglement measure at large scale compared with correlation
length is a tool to distinguish topological trivial and
nontrivial states. One of the ways to measure entanglement is
through topological entanglement entropy, $S_{top}=log D$, where
$D$ is the quantum dimension. The state is topological trivial
if and only if $D=1$. But it seems that this method can not be
applied to distinguish nontrivial states. For example, for FQH
state with filling factor $v=1/q$, $D=\sqrt{q}$, indicating that
it is nontrivial. But we know that FQH ground state has $q$ fold
degeneracy, all of them are nontrivial. My question is how to
distinguish between long range entangled states in a
quantitative way.  share|improve this question add comment  2
Answers  The quantum dimension is one such measure. The
different ground states of a particular