I will show that the periodically driven Ising chain in transverse field, for some particular values of the couplings, can be regarded as a minimal model for many body quantum chaos. Specifically, I will present an exact proof of the fact that the spectral form factor (a measure of spectral correlations) is described by random matrix theory. This result implies ergodicity for any finite amount of disorder in the longitudinal field, excluding the possibility of many-body localisation. The method used provides a novel route for obtaining exact non-perturbative results in non-integrable systems. As an example of this, I provide exact results on the entanglement spreading from a class of initial states and use that to characterise the entanglement spreading in the system.

References:

B. Bertini, P. Kos, and T. Prosen, arXiv:1812.05090

B. Bertini, P. Kos, and T. Prosen, Phys. Rev. Lett. 121, 264101(2018)