We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.

中文翻译：

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适用于多体定位的通用光谱形状因数

我们从理论上研究了在多体本地化系统的光谱中存在的相关性。可以得到泊松光谱的光谱形状因子的精确解析表达式，并与两个显示多体定位的模型的数值结果很好地吻合：无序量子自旋链和现象学$升$位模型基于运动的局部积分的存在。我们还确定了对状态的全局密度以及频谱边缘效应不敏感的通用机制。