A most important theme in condensed matter physics is how to characterize the fundamental states of quantum matter. The celebrated paradigms include Landau symmetry-breaking and topological quantum phases, whose characterizations have been broadly developed based on the equilibrium theories over the past half century. In comparison, the non-equilibrium quantum dynamics are far less understood. In this talk, I will present pedagogically a generic theory to characterize the far-from-equilibrium quantum dynamics induced in topological quantum systems, by showing a universal correspondence between equilibrium topological phases and non-equilibrium quantum dynamics, which in turn provides the non-equilibrium characterization of equilibrium topological phases. This generic theory is built on the so-called dynamical bulk-surface correspondence, which connects dD bulk topology of an equilibrium phase to topological pattern of quench dynamics emerging in the (d-1)D subspace, dubbed band-inversion surfaces (BISs), rendering a momentum-space counterpart of the well-known bulk-boundary correspondence for equilibrium topological phases in the real space. This dynamical bulk-surface correspondence can be extended to broad topological systems, including the correlated phases, Floquet phases, and the full Atland-Zirnbauer ten-fold symmetry classes. The rich nontrivial and universal far-from-equilibrium topological dynamics can be predicted. These results also provide conceptually new schemes to detect equilibrium topological phases by non-equilibrium quantum dynamics, which exhibit clear advantages in the detection and show the capabilities beyond equilibrium schemes. Finally, the future interesting issues will be commented.

报告人介绍：Xiong-Jun Liu received Ph.D in Texas A&M University in 2011, and was a postdoctoral fellow in University of Maryland, IAS HKUST and MIT (2011-2014). He joined the faculty of International Center for Quantum Materials at Peking University (09/2014), became tenured (07/2018), and now is a full professor (from 02/2019). He works in condensed matter theory and ultracold atoms, focusing on quantum simulation and topological matter: topological superconductors, synthetic gauge fields, non-equilibrium quantum systems, and strongly correlated topological states. He has been awarded the NSFC Distinguished Young Scholars (2018), and AAPPS-APCTP Chen-Ning Yang Award (2019).