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

<p>Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R&eacute;nyi 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&nbsp;<span class="math-tex">\(S(t) \propto t^{1/z}\)</span> where<br> the dynamical transport exponent z depends on the probability&nbsp;<span class="math-tex">\(\propto r^{-\alpha}\)</span> of gates spanning a distance r. For<br> sufficiently small <span class="math-tex">\(\alpha\)</span>, 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 L&eacute;vy flights. Our Letter sheds light on the connections between Clifford circuits and more generic<br> many-body quantum dynamics.</p>