  Recent progress in the study of many-body localization (MBL) in strongly
disordered interacting spin chains has emphasized the importance of
distinguishing finite time prethermal behavior from long time and large volume
asymptotics. We re-examine a reported non-ergodic extended (NEE) regime in the
interacting quasiperiodic Ganeshan-Pixley-Das Sarma model from this
perspective, and propose that this regime is a prethermal feature. Indeed, we
argue that the NEE regime may be identified through a change in the functional
form of spin-spin autocorrelation functions, demonstrating that the NEE regime
is distinguishable within intermediate-time dynamics. This is in contrast with
existing conjectures relating the NEE regime to the presence of an asymptotic
mobility edge in the single-particle spectrum. Thus, we propose a mechanism for
the formation of an NEE regime which does not rely on asymptotic properties of
the spin chain. Namely, we propose that the NEE regime emerges due to regularly
spaced deep wells in the disorder potential. The highly detuned sites suppress
spin transport across the system, effectively cutting the chain, and producing
a separation of time scales between the spreading of different operators. To
support this proposal, we show that the NEE phenomenology also occurs in random
models with deep wells but with no mobility edges, and does not occur in
quasiperiodic models with mobility edges but with no deep wells. Our results
support the broad conclusion that there is not a sharp distinction between the
dynamics of quasiperiodically and randomly disordered systems in the prethermal
regime. More specifically, we find that generic interacting quasiperiodic
models do not have stable intermediate dynamical phases arising from their
single-particle mobility edges, and that NEE phenomenology in such models is
transient.
