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