  We numerically investigate the dynamics of entanglement in a chain of
spinless fermions with nonrandom but long-range hopping and interactions, and
with random on-site energies. For moderate disorder in the absence of
interactions, the chain hosts delocalized states at the top of the band which
undergo a delocalization-localization transition with increasing disorder. We
find an interesting regime in this noninteracting disordered chain where the
long-time entanglement entropy scales as $S(t) \sim \ln t$ and the saturated
entanglement entropy scales with system size $L$ as $S(L,t \to {\infty}) \sim
\ln L$. We further study the interplay of long-range hopping and interactions
on the growth of entanglement and the many-body localization (MBL) transition
in this system. We develop an analogy to higher-dimensional short-range systems
to compare and contrast such behavior with the physics of MBL in a higher
dimension.
