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We study an effective Hamiltonian generating time evolution of states onintermediate time scales in the strong-coupling limit of the spin-1/2 XXZmodel. To leading order, it describes an integrable model with localinteractions. We solve it completely by means of a coordinate Bethe Ansatz thatmanifestly breaks the translational symmetry. We demonstrate the existence ofexponentially many jammed states and estimate their stability under the leadingcorrection to the effective Hamiltonian. Some ground state properties of themodel are discussed.

The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties