  We perform the fidelity analysis for Boltzmann-Gibbs-like states in order to
investigate whether the topological order of 1D fermionic systems at zero
temperature is maintained at finite temperatures. We use quantum walk protocols
that are known to simulate topological phases and the respective quantum phase
transitions for chiral symmetric Hamiltonians. Using the standard approaches of
the fidelity analysis and the study of edge states, we conclude that no
thermal-like phase transitions occur as temperature increases, i.e., the
topological behaviour is washed out gradually. We also show that the behaviour
of the Uhlmann geometric factor associated to the considered fidelity exhibits
the same behaviour as the latter, thus confirming the results obtained using
the previously established approaches.
