AKLT-like states on the kagome lattice using tensor-network methods

Following our previous work in arχiv:1711-00036 on deformations of the spin-2 AKLT state on the square lattice, we study analogous states on the kagome lattice. In addition to modifying the AKLT construction as before by inserting an on-site deformation that breaks the construction's SU(2) symmetry down to O(2), we alter the "bond states," considering not only the original singlet state but also triplet states oriented parallel or perpendicular to the symmetry axis of the deformation. Although these cases are equivalent when the state is constructed on a bipartite lattice, they are not when, as here, lattice frustration is present. This leaves us with three different phase diagrams, which we obtain using tensor-network methods. The first two appear at first to be completely featureless, and require further study to understand their physics. In the third, we find two different ferromagnetic phases: one polarized along the axis of the deformation, and one polarized along the axis of the bond state.