Disordered impenetrable two-component fermions in one dimension

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion ($t\ensuremath{-}0$ model) in presence of disorder. Our analytical treatment demonstrates that type disorder drastically changes nature emerging phases. The case spin-independent can be treated as a single-particle problem Anderson localization. On contrary, recent numerical findings show spin-dependent disorder, which realized random magnetic field, leads to many-body localization-delocalization transition. find an explicit analytic expression matrix elements field between eigenstates $t\ensuremath{-}0$ potential on finite lattice. Analysis supports existence transition this system and provides extended physical picture field.