Condensed Matter Theory Center and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2019 Oct 18;123(16):165902. doi: 10.1103/PhysRevLett.123.165902.
We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with subballistic operator spreading. The critical disorder strength for the ballistic to subballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the transition from subballistic to logarithmic behavior at the actual eigenstate localization transition is not resolved in our finite numerics. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.
我们研究了量子信息混乱，特别是使用矩阵乘积算子动力学在大无序自旋链中测量海森堡算符的增长，以扫描热化-局域量子相变。我们观察到弱无序时的弹道算子增长，以及向具有亚弹道算子扩展的相的急剧转变。从小链中能量本征态纠缠熵的有限尺寸标度确定，弹道到亚弹道转变的临界无序强度远低于多体局域相变。相比之下，我们发现，在实际本征态局域化转变处，从亚弹道到对数行为的转变在我们的有限数值中无法分辨。这些数据在增长算子形状的通用形式的背景下进行了讨论，并通过稀有区域的简单唯象模型得到了证实。
