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

TL;DR

This paper investigates the robustness of topological order in 1D fermionic systems at finite temperatures using quantum walk protocols, fidelity analysis, and Uhlmann geometric factors, finding gradual loss of topological features without sharp thermal phase transitions.

Contribution

It introduces a fidelity and Uhlmann geometric analysis framework to study topological phase stability at finite temperatures in quantum walk simulated systems.

Findings

No sharp thermal phase transitions observed with increasing temperature.

Topological behavior gradually diminishes as temperature rises.

Uhlmann geometric factor mirrors fidelity results, confirming the findings.

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.