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Fidelity and Uhlmann connection analysis of topological phase transitions in two dimensions

Mera, B. ; Amin, S. T. ; Vlachou, C. V. ; Paunkovic, N. ; Vieira, V.

Physical Review B - Condensed Matter and Materials Physics Vol. 98, Nº 24, pp. 245141-1 - 245141-19, December, 2018.

ISSN (print): 1098-0121
ISSN (online):

Journal Impact Factor: 3,736 (in 2014)

Digital Object Identifier: 10.1103/PhysRevB.98.245141

Abstract
We study the behavior of the fidelity and the Uhlmann connection in two-dimensional systems of free fermions that exhibit nontrivial topological behavior. In particular, we use the fidelity and a quantity closely related to the Uhlmann factor in order to detect phase transitions at zero and finite temperature for topological insulators and superconductors. We show that at zero temperature both quantities predict quantum phase transitions: a sudden drop of fidelity indicates an abrupt change of the spectrum of the state, while the behavior of the Uhlmann connection signals equally rapid change in its eigenbasis. At finite temperature, the topological features are gradually smeared out, indicating the absence of finite-temperature phase transitions, which we further confirm by performing a detailed analysis of the edge states. Moreover, we performed both analytical and numerical analysis of the fidelity susceptibility in the thermodynamic limit, providing an explicit quantitative criterion for the existence of phase transitions. The critical behavior at zero temperature is further analyzed through the numerical computation of critical exponents.