论文标题
通过纠缠增长在量子混乱上的拓扑下限
Topological lower bound on quantum chaos by entanglement growth
论文作者
论文摘要
现代量子混乱理论的基本结果是Maldacena-Shenker-Stanford鞋面的上限限制了超级阶段相关器的生长，其无限温度限制与进化操作员的操作员空间纠缠熵有关。在这里，我们表明，对于一维量子细胞自动机（QCA），存在通过这种纠缠熵量化的量子混乱的下限。该下限等于QCA的索引的两倍，QCA是一个拓扑不变的，可测量信息流的手性，并为所有rényi熵提供，其最强的rényi-$ \ infty $版本紧密。严格的界限排除了任何均方根纠缠生长行为的可能性，特别表明，对于显示非零指数的单一演变而禁止多体定位。由于Rényi熵是可以测量的，因此我们的发现具有直接的实验性相关性。我们的结果是针对指数尾巴的强大，这些尾巴自然出现在当地的哈密顿人产生的量子动力学中。
A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the evolution operator. Here we show that, for one-dimensional quantum cellular automata (QCA), there exists a lower bound on quantum chaos quantified by such entanglement entropy. This lower bound is equal to twice the index of the QCA, which is a topological invariant that measures the chirality of information flow, and holds for all the Rényi entropies, with its strongest Rényi-$\infty$ version being tight. The rigorous bound rules out the possibility of any sublinear entanglement growth behavior, showing in particular that many-body localization is forbidden for unitary evolutions displaying nonzero index. Since the Rényi entropy is measurable, our findings have direct experimental relevance. Our result is robust against exponential tails which naturally appear in quantum dynamics generated by local Hamiltonians.
