Classification of Mixed State Topology in One Dimension

Abstract

We show how to generalize the concepts of identifying and classifying symmetry protected topological phases in 1D to the case of an arbitrary mixed state. The pure state concepts are reviewed using a concrete spin-1 model. For the mixed state setup we demonstrate our findings numerically using matrix product state algorithms. Starting from the ground state and applying various types of noise sources we find a transient regime where the system is driven out of equilibrium while retaining its topological properties.

4 pages + appendix

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Cited by in corpus (13)

• Symmetry-protected Topological Phases at Finite Temperature
• Topological order of mixed states in quantum many-body systems
• Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
• Chern number and Berry curvature for Gaussian mixed states of fermions
• Topological characterization of one-dimensional open fermionic systems
• Reviving the Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• ${\mathbb{Z}}_2$ topological invariants for mixed states of fermions in time-reversal invariant band structures
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Efficient separation of quantum from classical correlations for mixed states with a fixed charge
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system