Universal topological quench dynamics: Altland-Zirnbauer tenfold classes

• URL: http://arxiv.org/abs/2104.00617v2
• Date: Wed, 7 Apr 2021 16:14:28 GMT
• Title: Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Authors: Lin Zhang, Wei Jia, Xiong-Jun Liu
• Abstract summary: Topological phases of the famous Altland-Zirnbauer (AZ) tenfold classes are defined on the equilibrium ground states. This work establishes a universal dynamical characterization for the complete AZ symmetry classes of topological phases.
• Score: 11.012609338912506
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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