Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature

Abstract

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.