Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
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DOI：
10.1103/physrevx.8.031057
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发表时间：
2018-09-07
影响因子：
12.5
通讯作者：
Huse, David A.
中科院分区：
文献类型：
--
作者：
Khemani, Vedika;Vishwanath, Ashvin;Huse, David A.
研究了混沌多体系统中局部守恒量（如扩散运动的电荷或能量）存在时局部量子信息的置乱。守恒定律和置乱之间的相互作用揭示了可逆的酉量子动力学产生缓慢耗散过程的扩散流体动力学的机制。我们在一个随机量子电路模型中得到了我们的结果，这个模型被约束于一个守恒定律。我们发现，一般扩散算子由两部分组成：(i)守恒部分包括局部守恒密度上扩散算子的权值，其动力学用扩散电荷扩散来描述；这个保守的部分也作为一个源，稳定地发射（ii）非保守算子的通量。这种发射导致算符流体力学中的耗散，耗散过程是算符权重从局部守恒算符到非守恒算符的缓慢转换，其速率由局部扩散电流设定。发射的非守恒部分然后以蝴蝶速度弹道扩散，因此变得高度非局部，因此基本上是不可观察的，从而充当促进耗散的“水库”。此外，我们发现，由于守恒分量的缓慢动力学，非守恒分量在其领先的弹道前沿后面发展出幂律尾巴。这意味着两个初始分离算子之间的过时序换向子在弹道前沿到达时急剧增长，但是，与没有守恒律的系统相比，它发展出扩散尾，并且仅以时间的幂次而不是指数方式接近其渐近晚时值。我们还在包含多个耦合扩散方程的有效流体动力学描述中推导了这些结果。
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a slow dissipative process. We obtain our results in a random quantum circuit model that is constrained to have a conservation law. We find that a generic spreading operator consists of two parts: (i) a conserved part which comprises the weight of the spreading operator on the local conserved densities, whose dynamics is described by diffusive charge spreading; this conserved part also acts as a source that steadily emits a flux of (ii) nonconserved operators. This emission leads to dissipation in the operator hydrodynamics, with the dissipative process being the slow conversion of operator weight from local conserved operators to nonconserved, at a rate set by the local diffusion current. The emitted nonconserved parts then spread ballistically at a butterfly speed, thus becoming highly nonlocal and, hence, essentially nonobservable, thereby acting as the "reservoir" that facilitates the dissipation. In addition, we find that the nonconserved component develops a power-law tail behind its leading ballistic front due to the slow dynamics of the conserved components. This implies that the out-of-time-order commutator between two initially separated operators grows sharply upon the arrival of the ballistic front, but, in contrast to systems with no conservation laws, it develops a diffusive tail and approaches its asymptotic late-time value only as a power of time instead of exponentially. We also derive these results within an effective hydrodynamic description which contains multiple coupled diffusion equations.