Many-body Quantum Chaos and Spectral Form Factor

The study of spectral statistics is of importance in physics due to its simplicity, universality, and utility as a diagnosis of quantum chaos and localization. Recently, as a probe of spectral statistics, the spectral form factor (SFF) has been instrumental in pinpointing novel signatures of many-body quantum chaos [1], in demonstrating the random matrix theory behaviour of black holes [2], and in shedding light on the existence of the many-body localization phase in the thermodynamic limit [3]. In this talk, I will give an overview on the generic behavior of the SFF in closed [4] and open [5] strongly-interacting many-body quantum chaotic systems, and its experimental measurements in quantum simulators [6].

References:

[1] AC, De Luca, and Chalker, PRL 121, 060601 (2018).

[2] Cotler et al., JHEP 1705:118 (2017).

[3] Šuntajs, Bonča, Prosen, and Vidmar, PRE 102, 062144 (2020).

[4] Shivam, De Luca, Huse, and AC, PRL 130, 140403 (2023)

[5] Li, Prosen, AC, PRL 127, 170602 (2021).

[6] Dong et al. w/ AC, arXiv:2403.16935 (2024).