Symmetry-protected topological corner modes in a periodically driven interacting spin lattice

Abstract

Periodic driving has the longstanding reputation for generating exotic phases of matter with no static counterparts. This work explores the interplay among periodic driving, interaction effects, and $\mathbb{Z}_2$ symmetry that leads to the emergence of Floquet symmetry protected second-order topological phases in a simple but insightful two-dimensional spin-1/2 lattice. Through a combination of analytical and numerical treatments, we verify the formation of 0 and $\pi$ modes, i.e., corner localized $\mathbb{Z}_2$ symmetry broken operators that respectively commute and anticommute with the one-period time evolution operator. We further verify the topological nature of these modes by demonstrating their presence over a wide range of parameter values and explicitly deriving their associated topological invariants under special conditions. Finally, we propose a means to detect the signature of such modes in experiments and discuss the effect of imperfections.