Universal topological quench dynamics for Z₂ topological phases

The free-fermion topological phases with Z₂ invariants cover a broad range of topological states, including the time-reversal invariant topological insulators, and 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 these equilibrium topological phases of different dimensionality and symmetry classes in the tenfold way, with a general framework being established. We show a novel result that a generic d-dimensional topological phase represented by Dirac type Hamiltonian and with Z₂ invariant defined on high symmetry momenta can be characterized by topology reduced to certain arbitrary discrete momenta of Brillouin zone called the highest-order band-inversion surfaces. Such dimension-reduced topology has unique correspondence to the topological pattern 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 completes the dynamical characterization for the full tenfold classes of topological phases, which can be partially extended to even broader topological phases protected by lattice symmetries and in non-Dirac type systems, and shall advance widely the research in theory and experiment.