Universal topological quench dynamics: Altland-Zirnbauer tenfold classes

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.

6+11 pages; 3+6 figures; 2 tables; Discussions are improved and typos are corrected

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• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Unconventional hybrid-order topological insulators
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Distinguishing dynamical quantum criticality through local fidelity distances
• Ultracold atomic lattice systems for simulating topological phases: A review
• Non-Markovianity Benefits Quantum Dynamics Simulation