  A symmetry-protected topologically ordered phase is a short-range entangled
state, for which some imposed symmetry prohibits the adiabatic deformation into
a trivial state which lacks entanglement. In this paper we argue that
magnetization plateau states of one-dimensional antiferromagnets which satisfy
the conditions $S-m\in$ odd integer, where $S$ is the spin quantum number and
$m$ the magnetization per site, can be identified as symmetry-protected
topological states if an inversion symmetry about the link center is present.
This assertion is reached by mapping the antiferromagnet into a nonlinear sigma
model type effective field theory containing a novel Berry phase term (a total
derivative term) with a coefficient proportional to the quantity $S-m$, and
then analyzing the topological structure of the ground state wave functional
which is inherited from the latter term. A boson-vortex duality transformation
is employed to examine the topological stability of the ground state in the
absence/presence of a perturbation violating link-center inversion symmetry.
Our prediction based on field theories is verified by means of a numerical
study of the entanglement spectra of actual spin chains, which we find to
exhibit twofold degeneracies when the aforementioned condition is met. We
complete this study with a rigorous analysis using matrix product states.
