Data of the publication "Transport and entanglement growth in long-range random Clifford circuits"

Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U(1) symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different
hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to \(S(t) \propto t^{1/z}\) where
the dynamical transport exponent z depends on the probability \(\propto r^{-\alpha}\) of gates spanning a distance r. For
sufficiently small \(\alpha\), we show that the presence of hydrodynamic modes becomes irrelevant such that S(t) behaves
similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator
spreading in U(1)-symmetric Clifford circuits where the emerging light cones can be understood in the context
of classical Lévy flights. Our Letter sheds light on the connections between Clifford circuits and more generic
many-body quantum dynamics.