Unsplit Spreading: An Overlooked Signature of Long-Range Interaction

Abstract

In conventional lattice models, the dispersion relation $ω(k)$ is assumed to be a smooth function. We prove that this smoothness implies the splitting of an initially localized excitation into counter-propagating wave packets. Consequently, unsplit spreading can occur only when $ω(k)$ develops singular features, precisely what long-range interactions enable. Remarkably, this phenomenon was clearly visible in published quantum simulation experiments as early as 2014, yet it has remained unrecognized or discussed as a distinct physical effect. We show that unsplit spreading emerges in realistic open quantum systems, such as 1D and 2D subwavelength atomic arrays, where the long-lived subradiant states host effective dispersion with the required singularities. Our work establishes unsplit spreading as an experimentally accessible, smoking-gun signature of singular band structure induced by long-range physics.