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The many-body localization (MBL) transition is a quantum phase transitioninvolving highly excited eigenstates of a disordered quantum many-bodyHamiltonian, which evolve from "extended/ergodic" (exhibiting extensiveentanglement entropies and fluctuations) to "localized" (exhibiting area-lawscaling of entanglement and fluctuations). The MBL transition can be driven bythe strength of disorder in a given spectral range, or by the energy density atfixed disorder - if the system possesses a many-body mobility edge. Here wepropose to explore the latter mechanism by using "quantum-quench spectroscopy",namely via quantum quenches of variable width which prepare the state of thesystem in a superposition of eigenstates of the Hamiltonian within acontrollable spectral region. Studying numerically a chain of interactingspinless fermions in a quasi-periodic potential, we argue that this system hasa many-body mobility edge; and we show that its existence translates into aclear dynamical transition in the time evolution immediately following a quenchin the strength of the quasi-periodic potential, as well as a transition in thescaling properties of the quasi-stationary state at long times. Our resultssuggest a practical scheme for the experimental observation of many-bodymobility edges using cold-atom setups.

Detecting a many-body mobility edge with quantum quenches