Topological edge modes without symmetry in quasiperiodically driven spin chains

TL;DR

This paper introduces a quasiperiodically driven spin chain model where edge states are protected by emergent dynamical symmetries, enabling stable quantum information storage without relying on microscopic symmetry protection.

Contribution

It demonstrates the existence of emergent dynamical symmetry-protected topological order in quasiperiodic systems, distinct from Floquet systems, and explores its stability and boundary criticality.

Findings

Edge states can store quantum information protected by emergent dynamical symmetries.

EDSPT order is stable up to stretched-exponential long times and possibly beyond.

Boundary dynamics can transition from quasiperiodic to chaotic, causing bulk thermalization.

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.