| Summary: | We study the disconnected entanglement entropy, $S^D$, of the
Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and
disconnected bipartite entanglement entropies that removes all area and volume
law contributions, and is thus only sensitive to the non-local entanglement
stored within the ground state manifold. Using analytical and numerical
computations, we show that $S^D$ behaves as a topological invariant, i.e., it
is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and
non-trivial phases, respectively. These results also hold in the presence of
symmetry-preserving disorder. At the second-order phase transition separating
the two phases, $S^D$ displays a system-size scaling behavior akin to those of
conventional order parameters, that allows us to compute entanglement critical
exponents. To corroborate the topological origin of the quantized values of
$S^D$, we show how the latter remain quantized after applying unitary time
evolution in the form of a quantum quench, a characteristic feature of
topological invariants.
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