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.

• Received 6 November 2020
• Revised 9 January 2021
• Accepted 11 January 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.L012019

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Published by the American Physical Society