论文标题
运算符在量子硬核气体中传播
Operator spreading in quantum hardcore gases
论文作者
论文摘要
在本文中，我们研究了一组具有任意局部希尔伯特空间维度的量子硬核气体（QHCG）的量子型核心气体（QHCG），并讨论基于基于矩阵的产品ANSATZ的方法，用于解决本地操作员分析的动态。随后，我们专注于操作员扩散的动力学，特别是在超时有序相关功能（OTOC），操作员重量扩散和操作员空间纠缠熵（OSEE）上。所有数量都猜想提供了可集成系统和量子混乱的标志性特征。我们表明，在QHCG OTOC中扩散地扩散，并且在大型局部Hilbert空间维度的极限下，尽管它们具有一致性，但它们会随时间线性增加。另一方面，最近猜想的是，与操作员程度相关的操作员重量方面在可集成和通用系统中扩散地传播，但是在这两种情况下，其衰减似乎有所不同。我们观察到，QHCG中操作员重量方面的扩散与混乱，通用集成和自由系统明显不同，因为前部在长期限制中冻结。最后，我们讨论了QHCG中的OSEE，并表明它最多可以按时间增长，并根据相互作用的集成系统的猜想行为。
In this article we study a set of integrable quantum cellular automata,the quantum hardcore gases (QHCG), with an arbitrary local Hilbert space dimension, and discuss the matrix product ansatz based approach for solving the dynamics of local operators analytically. Subsequently, we focus on the dynamics of operator spreading, in particular on the out-of-time ordered correlation functions (OTOCs), operator weight spreading and operators space entanglement entropy (OSEE). All of the quantities were conjectured to provide signifying features of integrable systems and quantum chaos. We show that in QHCG OTOCs spread diffusively and that in the limit of the large local Hilbert space dimension they increase linearly with time, despite their integrability. On the other hand, it was recently conjectured that operator weight front, which is associated with the extent of operators, spreads diffusively in both, integrable and generic systems, but its decay seems to differ in these two cases. We observe that the spreading of the operator weight front in QHCG is markedly different from chaotic, generic integrable and free systems, as the front freezes in the long time limit. Finally, we discuss the OSEE in QHCG and show that it grows at most logarithmically with time in accordance with the conjectured behaviour for interacting integrable systems.
