Fading ergodicity meets maximal chaos

Fading ergodicity provides a theoretical framework for understanding deviations from the eigenstate thermalization hypothesis (ETH) near ergodicity-breaking transitions. In this work we demonstrate that the position of the ergodicity-breaking critical point in the quantum sun model coincides with the peak of the maximally divergent fidelity susceptibility. We further extend our analysis to the energy-resolved ergodicity-breaking transition associated with the many-body mobility edge. Specifically, we show that fidelity susceptibilities at energies away from the middle of the spectrum exhibit a divergent peak near the mobility edge. We argue that fading ergodicity provides a simple and accurate description of the ETH breakdown in the quantum sun model, which is accompanied with the emergence of a peak in fidelity susceptibility and the onset of maximal chaos at the ergodicity-breaking critical point.