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We perform the fidelity analysis for Boltzmann-Gibbs-like states in order toinvestigate whether the topological order of 1D fermionic systems at zerotemperature is maintained at finite temperatures. We use quantum walk protocolsthat are known to simulate topological phases and the respective quantum phasetransitions for chiral symmetric Hamiltonians. Using the standard approaches ofthe fidelity analysis and the study of edge states, we conclude that nothermal-like phase transitions occur as temperature increases, i.e., thetopological behaviour is washed out gradually. We also show that the behaviourof the Uhlmann geometric factor associated to the considered fidelity exhibitsthe same behaviour as the latter, thus confirming the results obtained usingthe previously established approaches.

journal of physics. a, mathematical and theoretical

Boltzmann-Gibbs states in topological quantum walks and associated  many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase  Transitions