  We study the 1D Kitaev chain with long range superconductive pairing terms at
a finite temperature where the system is prepared in a mixed state in
equilibrium with a heat reservoir maintained at a constant temperature $T$. In
order to probe the footprint of the ground state topological behavior of the
model at finite temperature, we look at two global quantities extracted out of
two geometrical constructions: the Uhlmann and the interferometric phase.
Interestingly, when the long-range effect dominates, the Uhlmann phase approach
fails to reproduce the topological aspects of the model in the pure state
limit; on the other hand, the interferometric phase, though has a proper pure
state reduction, shows a behaviour independent of the ambient temperature.
