论文标题
部分可观测时空混沌系统的无模型预测
Chaos and operator growth in 2d CFT
论文作者
论文摘要
我们通过由Virasoro发电机组成的liouvillian在进化下研究了零温度二维形成共形场理论（CFT）中的超级订购的相关器（OTOC）。在Arxiv：1812.08657中，对OTOC的生长进行了猜想，这是Krylov复杂性设置的OTOC的生长，这是对操作员生长的量度。后者随着指数$2α$的指数而生长，该指数$2α$在Lyapunov指数上设置了上限，$λ_l\ leq2α$。我们发现，对于二维零温度CFT，OTOC用Lyapunov指数呈指数衰减，该指数饱和该结合。我们表明，这些Virasoro发电机形成了CFT的模块化哈密顿量，并将一半的空间追踪。因此，这种模块化的哈密顿量的进化会导致零温度CFT中的热动力学。利用系统的热动力学，我们使用OTOC的分析性和有界性能在零温度CFT中得出该结合。
We study the out-of-time-ordered correlator (OTOC) in a zero temperature two dimensional conformal field theory (CFT) under evolution by a Liouvillian composed of the Virasoro generators. A bound was conjectured in arXiv:1812.08657 on the growth of the OTOC set by the Krylov complexity which is a measure of operator growth. The latter grows as an exponential of time with exponent $2α$, which sets an upper bound on the Lyapunov exponent, $λ_L \leq 2α$. We find that for a two dimensional zero temperature CFT, the OTOC decays exponentially with a Lyapunov exponent which saturates this bound. We show that these Virasoro generators form the modular Hamiltonian of the CFT with half space traced out. Therefore, evolution by this modular Hamiltonian gives rise to thermal dynamics in a zero temperature CFT. Leveraging the thermal dynamics of the system, we derive this bound in a zero temperature CFT using the analyticity and boundedness properties of the OTOC.
