Universal topological quench dynamics: Altland-Zirnbauer tenfold classes

TL;DR

This paper establishes a universal framework linking equilibrium topological phases in all Altland-Zirnbauer classes to their far-from-equilibrium quantum dynamics through quench processes, revealing topological patterns in dynamical behavior.

Contribution

It introduces a universal topological quench dynamics framework applicable to all AZ tenfold classes, connecting equilibrium topology to non-equilibrium quantum dynamics.

Findings

Topological invariants are characterized by high-symmetry momentum points.

Dimension-reduced topology emerges at band-inversion surfaces.

Universal dynamical patterns serve as hallmarks of equilibrium topological phases.

Abstract

Topological phases of the famous Altland-Zirnbauer (AZ) tenfold classes are defined on the equilibrium ground states. Whether such equilibrium topological phases have universal correspondence to far-from-equilibrium quantum dynamics is a fundamental issue of both theoretical and experimental importance. Here we uncover the universal topological quench dynamics linking to the equilibrium topological phases for the complete AZ tenfold classes, with a general framework being established. We show a fundamental result that a $d$-dimensional topological phase of the tenfold class, with an integer invariant or $\mathbb{Z}_{2}$ index defined on high symmetry momenta, is generically characterized by topology reduced to the highest-order band-inversion surfaces located at arbitrary discrete momenta of Brillouin zone. Such dimension-reduced topology is further captured by universal topological patterns emerging in far-from-equilibrium quantum dynamics by quenching the system from trivial phase to the topological regime, rendering the dynamical hallmark of the equilibrium topological phase. This work establishes a universal dynamical characterization for the complete AZ symmetry classes of topological phases, which has broad applications in theory and experiment.