Fading ergodicity meets maximal chaos: Breakdown of eigenstate thermalization at the ergodicity breaking transition

Fading ergodicity represents a theoretical framework to describe deviations from the eigenstate thermalization hypothesis (ETH) near ergodicity breaking transitions. In this Letter, considering the quantum sun model of the avalanche theory, we show that the breakdown of the ETH at the interaction-driven ergodicity breaking transition point gives rise to maximal chaos, indicated by the maximally divergent fidelity susceptibilities. We then extend our study to the energy-driven ergodicity breaking transition emerging at the many-body mobility edge. Specifically, we consider fidelity susceptibilities as functions of energy densities at a fixed interaction strength, and we show that they exhibit a maximally divergent peak in the vicinity of the mobility edge.