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<br> hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to \(S(t) \propto t^{1/z}\) where<br> the dynamical transport exponent z depends on the probability \(\propto r^{-\alpha}\) of gates spanning a distance r. For<br> sufficiently small \(\alpha\), we show that the presence of hydrodynamic modes becomes irrelevant such that S(t) behaves<br> similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator<br> spreading in U(1)-symmetric Clifford circuits where the emerging light cones can be understood in the context<br> of classical Lévy flights. Our Letter sheds light on the connections between Clifford circuits and more generic<br> many-body quantum dynamics.