Related Experiment Video
Updated: Feb 26, 2026

Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy
Published on: October 24, 2017
Uhlmann Connection in Fermionic Systems Undergoing Phase Transitions
Bruno Mera1,2,3, Chrysoula Vlachou3,4, Nikola Paunković3,4
1CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal.
Abstract:
We study the behavior of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyze some of the paradigmatic cases of topological insulators and superconductors in one dimension, as well as the BCS theory of superconductivity in three dimensions. We show that the Uhlmann connection signals phase transitions in which the eigenbasis of the state of the system changes. Moreover, using the established fidelity approach and the study of the edge states, we show the absence of thermally driven phase transitions in the case of topological insulators and superconductors. We clarify what is the relevant parameter space associated with the Uhlmann connection so that it signals the existence of order in mixed states. In addition, the study of Majorana modes at finite temperature opens the possibility of applications in realistic stable quantum memories. Finally, the analysis of the different behavior of the BCS model and the Kitaev chain, with respect to the Uhlmann connection, suggested that in realistic scenarios the gap of topological superconductors could also, generically, be temperature dependent.
Related Concept Videos
Phase Transitions
States of Matter and Phase Changes
Phase Transitions: Sublimation and Deposition
Phase Diagram
Phase Transitions: Vaporization and Condensation
Phase Transitions: Melting and Freezing

