论文标题
远程随机电路的运输和纠缠增长
Transport and entanglement growth in long-range random Clifford circuits
论文作者
论文摘要
保护定律可以限制孤立的量子系统中的纠缠动态，这体现在更高的rényi熵下。在这里，我们在一类带有U $（1）$对称性的远程随机电路中探索了这种现象，其中可以从扩散到超级延伸到超级延伸。我们揭示了不同的流体动力体制在渐近纠缠中反映了自己，根据$ s（t）\ propto t^{1/z} $，其中动态传输指数$ z $取决于概率$ \ propto r^{ - α} $的门的门的距离，跨度为a $ r $。对于足够小的$α$，我们表明流体动力模式的存在变得无关紧要，因此$ s（t）$的行为与有和没有保护定律的电路相似。我们从u $（1）$ - 对称的克利福德电路中散布的被抑制操作员来解释我们的发现，在古典莱维航班的背景下，可以理解新兴的光锥。我们的工作阐明了Clifford电路与更通用的多体量子动力学之间的连接。
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 $\propto r^{-α}$ of gates spanning a distance $r$. For sufficiently small $α$, 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 work sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics.
