Impact of drive harmonics on the stability of Floquet many-body localization

Inducing Shifted Edge Modes by the Spin‐Dependent Time‐Periodical Driving and the Corresponding Topological Phase Transitions

“…One pivotal method in realizing the dynamical synthetic gauge field lies in driving quantum systems periodically, which is also known as Floquet engineering. [ 1–9 ] The discrete time translational symmetry in Floquet engineering signifies that the systems periodically exchange energy (or particles) with the external driving field, and hence there exist no well defined ground states. In consequence, in contrast to the static cases, the topological characterizations of periodically driven systems are based on the Floquet evolving operator $$U(T)$$, of which the diagonalization may give birth to not only zero quasi‐energy edge modes, but also the Floquet edge modes pinned at quasi‐energy $$\pm \frac{\omega }{2}$$.…”