论文标题
量子纠缠和光谱形式
Quantum Entanglement and Spectral Form Factor
论文作者
论文摘要
我们在光谱形式和水平间距分布函数中用模块化的哈密顿量代替了哈密顿量。这项研究建立了量子纠缠中的数量与量子混乱之间的联系。要进行量子纠缠的通用研究，我们考虑了高斯随机2 Qubit模型。贝尔不平等的最大侵犯表明与纠缠熵有正相关。因此，违规起着等同的作用，作为量子纠缠。我们首先对量子纠缠量与倾角之间的关系进行分析估计，而该子区域只有一个量子。第一个倾角的时间是纠缠熵的单调。子区域中的动力学在很晚时独立于初始状态。它是经典混乱的信号传导条件之一。我们还将分析扩展到高斯随机3量状态，并表明结果相似。模拟表明，级别间距分布函数在晚期接近GUE。最后，我们将QFT的技术开发到与$ n $ -sheet歧管有关的光谱形式。我们将该技术应用于CFT $ _2 $的单个间隔，并以$ \ MATHCAL {N} = 4 $ SUPER YANG-MILLS理论中的球形纠缠表面应用。结果是两种情况之一，但是rényi熵可以取决于rényi指数。对于CFT $ _2 $的情况，它表示连续体和离散频谱之间的差异。
We replace a Hamiltonian with a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This study establishes a connection between quantities within Quantum Entanglement and Quantum Chaos. To have a universal study for Quantum Entanglement, we consider the Gaussian random 2-qubit model. The maximum violation of Bell's inequality demonstrates a positive correlation with the entanglement entropy. Thus, the violation plays an equivalent role as Quantum Entanglement. We first provide an analytical estimation of the relation between quantum entanglement quantities and the dip when a subregion only has one qubit. The time of the first dip is monotone for entanglement entropy. The dynamics in a subregion is independent of the initial state at a late time. It is one of the signaling conditions for classical chaos. We also extend our analysis to the Gaussian random 3-qubit state, and it indicates a similar result. The simulation shows that the level spacing distribution function approaches GUE at a late time. In the end, we develop a technique within QFT to the spectral form factor for its relation to an $n$-sheet manifold. We apply the technology to a single interval in CFT$_2$ and the spherical entangling surface in $\mathcal{N}=4$ super Yang-Mills theory. The result is one for both cases, but the Rényi entropy can depend on the Rényi index. For the case of CFT$_2$, it indicates the difference between the continuum and discrete spectrum.
