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Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping

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].