Tunable Statistics-Induced Caging in the Anyon-Hubbard Model
We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.