  In one-dimensional (1D) disorder-free interacting systems, a sufficiently
strong linear potential can induce localization of the many-body eigenstates, a
phenomenon dubbed as Stark many-body localization (MBL). In this paper, we
investigate the fate of Stark MBL in 1D spinless fermions systems with
long-range interactions, specifically focusing on the role of interaction
strength. We obtain the Stark MBL phase diagrams by computing the mean gap
ratio and many-body inverse participation ratio at half-filling. We show that,
for short-range interactions, there is a qualitative symmetry between the
limits of weak and strong interactions. However, this symmetry is absent in the
case of long-range interactions, where the system is always Stark many-body
localized at strong interactions, regardless of the linear potential strength.
Furthermore, we study the dynamics of imbalance and entanglement with various
initial states using time-dependent variational principle (TDVP) numerical
methods. We reveal that the dynamical quantities display a strong dependence on
the initial conditions, which suggests that the Hilbert-space fragmentation
precludes thermalization. Our results demonstrate the robustness of Stark MBL
even in the presence of long-range interactions and offer an avenue to explore
MBL in disorder-free systems with long-range interactions.
