  We study one-dimensional spinless fermions with random interactions, but
without any on-site disorder. We find that random interactions generically
stabilize a many-body localized phase, in spite of the completely extended
single-particle degrees of freedom. In the large randomness limit, we construct
"bubble-neck" eigenstates having a universal area-law entanglement entropy on
average, with the number of volume-law states being exponentially suppressed.
We argue that this statistical localization is beyond the phenomenological
local-integrals-of-motion description of many-body localization. With exact
diagonalization, we confirm the robustness of the many-body localized phase at
finite randomness by investigating eigenstate properties such as level
statistics, entanglement/participation entropies, and nonergodic quantum
dynamics. At weak random interactions, the system develops a thermalization
transition when the single-particle hopping becomes dominant.
