Z3 ferromagnet to Valence Bond Solid transition in 1d

We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we focus on the transition between Z3 ferromagnet and Valence Bond Solid (VBS) in a 1d chain with a Z3xZ3 global symmetry. We use a model with alternating projective representations on the sites of the two sublattices. This allows the model to connect to an exactly solvable point which has VBS character as SU(3)-invariant singlets. We find a direct transition from this phase to a ferromagnetically ordered phase breaking Z3 symmetry. Numerical evidence suggests a second-order or extremely weak first-order transition. We characterize the apparent criticality using entanglement scaling and the critical scaling of lattice operators.