Emergence of Topological States in Relaxation Dynamics of Interacting Bosons

Topological concepts have been employed to understand a wide range of phenomena in physics. While a plethora of ground states are known to have topological underpinning, it is still quite unclear if and how topology manifests itself in the relaxation dynamics of strongly correlated many-body systems. In this Letter, we study time evolution of interacting bosons in a finite one-dimensional superlattice and uncover surprising emergent topological phenomena in the long-time stationary states. Beginning with simple product states, the system evolves into stationary states with high energy whose string correlation and entanglement are investigated. Based on extensive numerical simulations and effective-model analysis, it is demonstrated that the stationary states are nonthermal for a wide range of parameters, and they exhibit certain features that are characteristic of the symmetry-protected topological ground state of the Hamiltonian. In contrast, no topological feature is found in the stationary state as long as the system thermalizes. This difference is further corroborated by the distinct behavior of quantum entanglement and edge states of the system. Our theoretical prediction can be examined by current experimental techniques and paves the way for a more comprehensive understanding of topological phases in nonequilibrium settings.