The Uhlmann connection in fermionic systems undergoing phase transitions

Abstract

We study the behaviour of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyse some of the paradigmatic cases of topological insulators and superconductors in dimension one, 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.

14 pages (including Supplemental Material); Updated with new results; Accepted for publication in Physical Review Letters

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Cited by in corpus (31)

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• Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states
• Fidelity and Uhlmann connection analysis of topological phase transitions in two dimensions
• Thermal Uhlmann Chern number from the Uhlmann connection for extracting topological properties of mixed states
• Topological characterization of one-dimensional open fermionic systems
• Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
• Finite temperature geometric properties of the Kitaev honeycomb model
• Haldane Model at finite temperature
• Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Topological order, mixed states and open systems
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Uhlmann quench and geometric dynamic quantum phase transition of mixed states
• Vanishing k-space fidelity and phase diagram's bulk-edge-bulk correspondence
• On critical properties of Berry curvature in Kitaev honeycomb model
• Thermal topological phase transition in SnTe from \emph{ab-initio} calculations
• Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators
• Information geometric analysis of long range topological superconductors
• Quantifying fermionic interactions from the violation of Wick's theorem
• Interferometric and Uhlmann phases of mixed polarization states
• Geometric phases of Topological Systems under Quench Process
• Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
• Geometrical properties of the ground state manifold in the spin boson model
• Thermal Uhlmann phase in a locally driven two-spin system
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Comparison of finite-temperature topological indicators based on Uhlmann connection