  We investigate the possibility of a many-body mobility edge in the
Generalized Aubry-Andr\'e (GAA) model with interactions using the Shift-Invert
Matrix Product States (SIMPS) algorithm (Phys. Rev. Lett. 118, 017201 (2017)).
The non-interacting GAA model is a one-dimensional quasiperiodic model with a
self-duality induced mobility edge. The advantage of SIMPS is that it targets
many-body states in an energy-resolved fashion and does not require all
many-body states to be localized for convergence, which allows us to test if
the interacting GAA model manifests a many-body mobility edge. Our analysis
indicates that the targeted states in the presence of the single particle
mobility edge match neither `MBL-like' fully-converged localized states nor the
fully delocalized case where SIMPS fails to converge. An entanglement-scaling
analysis as a function of the finite bond dimension indicates that the
many-body states in the vicinity of a single-particle mobility edge behave
closer to how delocalized states manifest within the SIMPS method.
