Geometric Phases for Mixed States of the Kitaev Chain

Abstract

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyze the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyze the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

Minor corrections; journal reference added

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Cited by in corpus (19)

• Geometry of quantum phase transitions
• Identification of symmetry-protected topological states on noisy quantum computers
• Observation of topological Uhlmann phases with superconducting qubits
• Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• The Uhlmann connection in fermionic systems undergoing phase transitions
• Topological characterization of one-dimensional open fermionic systems
• Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature
• Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
• Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases
• Non-Abelian Geometric Phases Carried by the Spin Fluctuation Tensor
• Thermal topological phase transition in SnTe from \emph{ab-initio} calculations
• Interferometric and Uhlmann phases of mixed polarization states
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Thermal Uhlmann phase in a locally driven two-spin system
• Mixed-state geometric phases of coherent and squeezed spin states
• Uhlmann phase in composite systems with entanglement
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics