Probing the mobility edge in an interacting model using MPS

The quasiperiodic Generalized Aubry-André model is known to exhibit a mobility edge in the noninteracting limit for a certain range of disorder strengths. However, there is not much known about the interacting version of the model. We use the Shift-Invert Matrix Product State method of Yu, Pekker, and Clark to study this system with sizes from 32 to 128 sites, computing excited states for different disorder realizations (produced by varying the phase in the quasiperiodic potentials). Our goal is to determine where many-body localized states are absent or present, starting from the single-particle mobility edge.