  Stark many body localization problem on a periodic spin chain with local four
spin hopping conserving dipole moment becomes equivalent to a spin pair hopping
model after overturn of spins in odd or even positions. Eigenstates of the
latter problem are separated into four groups including two groups of
delocalized states with translationally invariant unrestricted (group I) or
restricted (group II) Krylov subspaces and other two with confined spin
transport having either all mobile (group III) or some immobile spins (group
IV). These groups can be examined experimentally in systems like those recently
investigated in Refs. [1, 2].
