  We investigate the build-up of quasi-long-range order in the XX chain with
transverse magnetic field at finite size. As the field is varied, the ground
state of the system displays multiple level crossings producing a sequence of
entanglement jumps. Using the partial fidelity and susceptibility, we study the
transition to the thermodynamic limit and argue that the topological order can
be described in terms of kink-antikink pairs and marked by edge spin
entanglement.
