Topological order, mixed states and open systems

Abstract

The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states had received only quite recently attention in the literature. In particular, it is still unclear whether the generalisation of the Aharonov-Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse from a general viewpoint topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with a periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.

14 pages

References in corpus (5)

• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Topology of density matrices
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• Space, matter and topology

Cited by in corpus (11)

• Identification of symmetry-protected topological states on noisy quantum computers
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols
• Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states
• Schwinger's picture of Quantum Mechanics
• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures
• Topological classifications of quadratic bosonic excitations in closed and open systems with examples
• Geometry from divergence functions and complex structures
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes
• Comparison of finite-temperature topological indicators based on Uhlmann connection