Chiral Floquet Selection of an Algebraic Rydberg Bound State in the Continuum

Bound states in the continuum (BICs) remain localized despite the presence of extended modes at the same energy. In driven systems with long-range couplings, the absence of radiation does not by itself determine how a bound state decays in space. We study this problem in a Hermitian Rydberg spin waveguide, where a drive whose phase winds around a four-site plaquette combines rotation with time translation to exclude propagating guide channels from one symmetry sector. The resulting eigenstate remains embedded in the continuum of other sectors and carries an inverse-cube waveguide amplitude, with coherent contributions from direct plaquette–guide coupling and long-range guide propagation. Microscopic pair calculations determine the coupling in the axial Rydberg geometry, while coherent Floquet mixing accounts for the dominant angular-mode weight. The bound state thus retains the spatial signature of the long-range coupling even when radiation is forbidden.