Fragmentation of SU(2)-invariant spin ladders

A two-parameter family of quantum spin ladders with local bilinear and biquadratic interactions is shown to be solvable by a mapping onto fragments of integrable spin 1 chains. The phase diagram, consisting of four phases, and the ground state properties are discussed. In one novel phase, the ground state is made up of plaquette singlets and rung singlets, alternating with a three-rung periodicity.