Transport and entanglement growth in long-range random Clifford circuits

TL;DR

This paper investigates how conservation laws and long-range interactions influence entanglement growth in random Clifford circuits, revealing a dependence on transport regimes and the role of operator spreading.

Contribution

It demonstrates the relationship between transport properties and entanglement growth in long-range Clifford circuits with U(1) symmetry, highlighting the impact of long-range interactions.

Findings

Entanglement growth scales as $t^{1/z}$ depending on transport exponent z.

Hydrodynamic modes become irrelevant for small $\alpha$, making entanglement similar with or without conservation laws.

Operator spreading is inhibited and can be described by classical Lévy flights.

Abstract

Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R\'enyi 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 L\'evy flights. Our work sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics.