Investigating many-body mobility edges in isolated quantum systems

The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and intial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose non-interacting version known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, directly comparing it with the predictions of the Eigenstate Thermalization Hypothesis (ETH). Our results indicate the coexistence of regions with finite measure when approaching the thermodynamic limit where thermalization and localization are manifest, suggesting that one cannot explain their appearance as merely being a result of finite-size effects.