  We study the fate of many-body localization (MBL) in the presence of
long-range hopping ($\sim 1/r^{\sigma}$) in a system subjected to an electric
field (static and time-periodic) along with a slowly-varying aperiodic
potential. We show that the MBL in the static electric-field model is robust
against arbitrary long-range hopping in sharp contrast to other disordered
models, where MBL is killed by sufficiently long-range hopping. Next, we show
that the drive-induced phenomena associated with an ac square wave electric
field are also robust against long-range hopping. Specifically, we obtain
drive-induced MBL, where a high-frequency drive can convert the ergodic phase
into the MBL phase. Remarkably, we find that coherent destruction of MBL is
also possible with the aid of a resonant drive. Thus in both the static and
time-periodic square wave electric field models, the qualitative properties of
the system are independent of whether the hopping is short-ranged or
long-ranged.
