Abstract
The surprisingly long-lasting oscillations observed in the dynamics of highly excited states of chains of Rydberg atoms defy the expectation that interacting systems should thermalize fast. The phenomenon is reminiscent of wavepackets in quantum billiards that trace classical periodic orbits. While analogs of the associated scarred eigenfunctions have been found for Rydberg chains, an underlying classical limit hosting periodic orbits has remained elusive. Here we generalize the Rydberg (pseudospin S=1/2) system to a chain of arbitrary spin S. Its classical limit features unexpectedly stable periodic orbits that are essential to understand the emergence of robust, parametrically suppressed quantum chaoticity, with semi-classical coherence times diverging as √S. The classical limit successfully explains several empirical features of the quantum limit.