Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
Phys Rev Lett. 2019 Jan 18;122(2):020603. doi: 10.1103/PhysRevLett.122.020603.
We investigate how information spreads in three paradigmatic one-dimensional models with spatial disorder. The models we consider are unitarily related to a system of free fermions and, thus, are manifestly integrable. We demonstrate that out-of-time-order correlators can spread slowly beyond the single-particle localization length, despite the absence of many-body interactions. This phenomenon is shown to be due to the nonlocal relationship between elementary excitations and the physical degrees of freedom. We argue that this nonlocality becomes relevant for time-dependent correlation functions. In addition, a slow logarithmic-in-time growth of the entanglement entropy is observed following a quench from an unentangled initial state. We attribute this growth to the presence of strong zero modes, which gives rise to an exponential hierarchy of time scales upon ensemble averaging. Our work on disordered integrable systems complements the rich phenomenology of information spreading and we discuss broader implications for general systems with nonlocal correlations.
我们研究了信息在三个具有空间无序的典型一维模型中的传播方式。我们考虑的模型与自由费米子系统有单元关系，因此是明显可积的。我们证明，尽管不存在多体相互作用，但在时间外关联函数可以在单粒子局域化长度之外缓慢扩展。这种现象被证明是由于基本激发和物理自由度之间的非局域关系。我们认为这种非局域性对于时变相关函数变得很重要。此外，在从无纠缠初始状态进行淬火后，观察到纠缠熵以对数时间的速度缓慢增长。我们将这种增长归因于强零模的存在，这导致了在集合平均时出现指数时间尺度的层次结构。我们在无序可积系统方面的工作补充了信息传播的丰富现象学，并讨论了对具有非局域相关的一般系统的更广泛影响。
