Quantum chaos dynamics in long-range power law interaction systems
Quantum chaos dynamics in long-range power law interaction systems
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DOI：
10.1103/physrevb.100.064305
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发表时间：
2019-08-08
影响因子：
3.7
通讯作者：
Zhou, Tianci
中科院分区：
文献类型：
--
作者：
Chen, Xiao;Zhou, Tianci
利用一个无序交换子（OTOC）诊断一维长程幂律相互作用系统中混沌的传播。我们将OTOC的演化映射为一个经典的随机动力学问题，并使用布朗量子电路精确推导出主方程。我们改变两个参数：每个站点上的量子位数N（站点上的希尔伯特空间维度）和幂律指数alpha。OTOC在N = 1时出现三种光锥结构：（1）当0.5 <α小于或接近0.8时为对数，（2）当0.8小于或接近α小于或接近1.5时为次线性幂律，（3）当α大于或接近1.5时为线性。在前两种情况下，OTOC的尺度分别为exp（lambda t）/chi（2 alpha）和t（2 alpha/zeta）/chi（2 alpha），超出了光锥。当α>= 2时，OTOC具有与短程相互作用系统基本相同的扩散增宽，表明局部性完全恢复。在大N极限下，它总是一个对数光锥渐近，虽然线性光锥可以出现在α大于或接近1.5的过渡时间之前。这意味着对于有限的α，局部性永远不会完全恢复。我们的结果为长程幂律相互作用系统的混沌动力学提供了一个统一的物理图象。
We use an out-of-time-order commutator (OTOC) to diagnose the propagation of chaos in one-dimensional long-range power law interaction system. We map the evolution of OTOC to a classical stochastic dynamics problem and use a Brownian quantum circuit to exactly derive the master equation. We vary two parameters: The number of qubits N on each site (the on-site Hilbert space dimension) and the power law exponent alpha. Three light cone structures of OTOC appear at N = 1: (1) logarithmic when 0.5 < alpha less than or similar to 0.8, (2) sublinear power law when 0.8 less than or similar to alpha less than or similar to 1.5, and (3) linear when alpha greater than or similar to 1.5. The OTOC scales as exp(lambda t)/chi(2 alpha) and t(2 alpha/zeta) /chi(2 alpha), respectively, beyond the light cones in the first two cases. When alpha >= 2, the OTOC has essentially the same diffusive broadening as systems with short-range interactions, suggesting a complete recovery of locality. In the large N limit, it is always a logarithmic light cone asymptotically, although a linear light cone can appear before the transition time for alpha greater than or similar to 1.5. This implies the locality is never fully recovered for finite alpha. Our result provides a unified physical picture for the chaos dynamics in a long-range power law interaction system.