Topological edge modes without symmetry in quasiperiodically driven spin chains

We construct an example of a 1d quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. In a sharp departure from topological phases 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 timescales, 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 type of boundary critical with no known static or Floquet analogue, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

Automated summary

We construct an example of a 1d quasiperiodically driven spin chain that has edge states protected by a combination of localization, dynamics, and topology. The protection of the edge states is purely based on emergent dynamical symmetries, rather than microscopic symmetry protection. We investigate the dynamical signatures of this emergent dynamical symmetry-protected topological (EDSPT) order through computational methods and find evidence of its stability against bulk many-body localization.