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

Abstract

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.

arXiv comment15 pages, 5 figures, 1 table

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• Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
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• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Controllable simulation of topological phases and edge states with quantum walk
• Information geometric analysis of long range topological superconductors
• Thermal Uhlmann phase in a locally driven two-spin system