Quantum epidemiology: operator growth, thermal effects, and SYK
Quantum epidemiology: operator growth, thermal effects, and SYK
复制标题
DOI：
10.1007/jhep08(2019)012
复制
发表时间：
2018-10
影响因子：
5.4
通讯作者：
X. Qi;Alexandre Streicher
中科院分区：
文献类型：
--
作者：
X. Qi;Alexandre Streicher
摘要在多体混沌系统中，海森堡演化过程中算子的大小一般是增长的，它可以用某些非时序的四点函数来度量。然而，这些仅提供了对全部底层算子增长结构的粗略探测。在这篇文章中，我们开发了一种方法来推导完整的费米系统的生长结构，也自然地引入了有限温度的影响。然后，我们将我们的方法应用于SYK模型，该模型具有所有对所有体的相互作用。我们推导出了所有温度下大q极限下的完整算子增长结构。我们看到，它的温度依赖性有一个非常简单的形式一致的慢下来的混乱随着温度的降低。此外，我们的有限温度扰频结果可以通过修改的流行病模型来建模，其中热状态作为接种疫苗的群体，从而减缓了整体感染率。
AbstractIn many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure. In this article we develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-allq-body interactions. We derive the full operator growth structure in the largeqlimit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.