Superdiffusive to ballistic transport in nonintegrable Rydberg simulator

A common wisdom posits that transport of conserved quantities across clean nonintegrable quantum systems at high temperatures is diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter if the strong interaction limit is taken. Using Krylov-typicality and purification matrix-product-state methods, we establish in short-to-intermediate time scales the following observations for the nonintegrable lattice model imitating the experimental Rydberg blockade simulator. Given the strict projection owing to the infinite density-density repulsion V, the Rydberg chain’s energy transport in the presence of a transverse field g is tentatively superdiffusive at infinite temperature featured by an anomalous scaling exponent $$\frac{3}{4}$$ , indicating the potential existence of a novel dynamical universality class. Imposing, in addition, a growing longitudinal field h causes a putative superdiffusion-to-ballistic transport transition at h ≈ g. Interestingly, all the above results persist for large but finite interactions and temperatures, provided that the strongly interacting condition g, h ≪ kBT ≪ V is fulfilled. Our predictions are testable by current Rydberg quantum simulation facilities.