Topological edge modes without symmetry in quasiperiodically driven spin chains

Abstract

We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

7+8 pages, 5 figures

References in corpus (11)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Phenomenology of fully many-body-localized systems
• Many-body localization in periodically driven systems
• Periodically driven ergodic and many-body localized quantum systems
• Constructing local integrals of motion in the many-body localized phase
• Protection of topological order by symmetry and many-body localization
• Eigenstate phases with finite on-site non-Abelian symmetry
• Many-Body Localization of Symmetry Protected Topological States
• Very slow heating for weakly driven quantum many-body systems

Cited by in corpus (19)

• Long-range interacting quantum systems
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Biology and medicine in the landscape of quantum advantages
• Realizing a dynamical topological phase in a trapped-ion quantum simulator
• Many-Body Localization with Quasiperiodic Driving
• Observation of topological prethermal strong zero modes
• Topological edge states at Floquet quantum criticality
• Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Self-similar phase diagram of the Fibonacci-driven quantum Ising model
• Anomalous Random Multipolar Driven Insulators
• Gapless higher-order topology and corner states in Floquet systems
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• A matrix product operator approach to non-equilibrium Floquet steady states
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Emergence of quasiperiodic behavior in transport and hybridization properties of clean lattice systems