Fragility of Time-Reversal Symmetry Protected Topological Phases

Abstract

The second law of thermodynamics points to the existence of an `arrow of time', along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators and the Haldane phase of quantum magnets. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes which would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility, but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics, and elucidate potential challenges in utilising topological systems for quantum technologies.

arXiv comment3 + 4 Pages, 1 Figure. Accepted version

References in corpus (32)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Exceptional Topology of Non-Hermitian Systems
• Entanglement spectrum of a topological phase in one dimension
• Majorana Zero Modes and Topological Quantum Computation
• Nonlocal edge state transport in the quantum spin Hall state
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Concepts and methods in the theory of open quantum systems
• Symmetry Protected Topological phases of Quantum Matter
• Topology by Dissipation in Atomic Quantum Wires
• The approach to thermal equilibrium in quantized chaotic systems
• Stability and instability towards delocalization in MBL systems
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Detection of Symmetry Protected Topological Phases in 1D
• Majorana qubit decoherence by quasiparticle poisoning
• Topology by dissipation
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Inelastic electron backscattering in a generic helical edge channel
• Tenfold Way for Quadratic Lindbladians
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Phonon induced backscattering in helical edge states
• Decay rates for topological memories encoded with Majorana fermions
• Classification of topological insulators and superconductors out of equilibrium
• Noise-induced backscattering in a quantum-spin-Hall edge
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Irreducible Projective Representations and Their Physical Applications

Cited by in corpus (29)

• Symmetry classes of open fermionic quantum matter
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Intrinsic Mixed-state Topological Order
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Rapid thermalization of spin chain commuting Hamiltonians
• Interplay between friction and spin-orbit coupling as a source of spin polarization
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Stability of Time-Reversal Symmetry Protected Topological Phases
• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Cooper-pair transistor as a minimal topological quantum circuit
• Persistence of Topological Phases in Non-Hermitian Quantum Walks
• Kramers' degeneracy for open systems in thermal equilibrium
• Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Edge modes and symmetry-protected topological states in open quantum systems
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Elastic backscattering of quantum spin Hall edge modes from Coulomb interactions with non-magnetic impurities
• Topologically Ordered Steady States in Open Quantum Systems
• Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
• Dissipative Symmetry-Protected Topological Order
• Mixed-state phase transitions in spin-Holstein models
• Steady-state topological order
• Edge spin transport in the disordered two-dimensional topological insulator WTe${}_2$
• Fate of symmetry protected coherence in open quantum system
• Time-reversal symmetry breaking and emergence in driven-dissipative Ising models
• Robust nonequilibrium edge currents with and without band topology
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Time-dependent driving and topological protection in the fractional Josephson effect
• Robust nonequilibrium surface currents in the 3D Hofstadter model