  We numerically study the random-hopping fermions (the Cruetz ladder) with
repulsion and investigate how the interactions deform localized eigenstates by
means of the one particle-density matrix (OPDM). The ground state exhibits
resurgence of localization from the compact localized state to
strong-repulsion-induced localization. On the other hand, excited states in the
middle of the spectrum tend to extend by the repulsion. The transition property
obtained by numerical calculations of the OPDM is deeply understood by studying
a solvable model in which local integrals of motion (LIOMs) are obtained
explicitly. The present work clarifies the utility of the OPDM and also how
compact-support LIOMs in non-interacting limit are deformed by the repulsion.
