Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium

Abstract

The time evolution of topological systems is an active area of interest due to their expected applications in fault-tolerant quantum computing. Here, we analyze the dynamics of a noninteracting spinless fermion chain in its topological phase, quenched out of equilibrium by a Hamiltonian belonging to the same symmetry class. Due to particle-hole symmetry, the bulk properties of the system remain intact throughout its evolution. However, the boundary properties may be drastically altered, with the initially localized Majorana edge modes extending across the chain. Up to a timescale $t^{\ast }$, identified by area-law behavior of the entanglement entropy, these extended edge modes are an example of exotic effects in topological systems out of equilibrium. Further, while local disorder can be utilized to preserve localization and increase $t^{\ast }$, we still identify nontrivial dynamics in the Majorana polarization and Loschmidt echo.

arXiv comment16 pages, 7 figures. Reformatted as a longer-form article by including, in the main text, some material previously in the supplementary materials. Additional details have also been added, including an extended discussion of the return rate where we isolate the boundary contribution

References in corpus (53)

• Unpaired Majorana fermions in quantum wires
• Topological Field Theory of Time-Reversal Invariant Insulators
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Classification of topological quantum matter with symmetries
• Entanglement in quantum critical phenomena
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Calculation of reduced density matrices from correlation functions
• An Area Law for One Dimensional Quantum Systems
• Effective quantum spin systems with ion traps
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Reduced density matrices and entanglement entropy in free lattice models
• Dynamical quantum phase transitions: a review
• Symmetry Protected Topological phases of Quantum Matter
• Environment-independent decoherence rate in classically chaotic systems
• Entanglement spectrum of topological insulators and superconductors
• Single particle Green's functions and interacting topological insulators
• Realization of a minimal Kitaev chain in coupled quantum dots
• Dynamical Topological Order Parameters far from Equilibrium
• Topological classification of dynamical phase transitions
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Bulk-Edge Correspondence in the Entanglement Spectra
• Topological invariants and interacting one-dimensional fermionic systems
• An area law for entanglement from exponential decay of correlations
• AIII and BDI Topological Systems at Strong Disorder
• Dynamical topological invariant after a quantum quench
• Topology of one dimensional quantum systems out of equilibrium
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization
• A bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors
• Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
• Classification of topological insulators and superconductors out of equilibrium
• Topological Quantum Liquids with Long-Range Couplings
• Quench dynamics and parity blocking in Majorana wires
• Topology and entanglement in quench dynamics
• Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• Signatures of topology in quantum quench dynamics and their interrelation
• Hybrid Topological Quantum Computation with Majorana Fermions: A Cold Atom Setup
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Dynamical Phase Transitions in Topological Insulators
• Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
• Quench Dynamics of Topological Maximally-Entangled States
• Disorder-induced topology in quench dynamics
• Generic theory of characterizing topological phases under quantum slow dynamics
• An Interplay of Topology and Quantized Geometric Phase for two Different Symmetry-Class Hamiltonians
• Manifestation of a topological gapless phase in a two-dimensional chiral symmetric system through Loschmidt echo
• Dynamical characterization of topological phases beyond the minimal models