Exactly solvable model for a deconfined quantum critical point in 1D

We construct an exactly solvable lattice model for a deconfined quantum critical point (DQCP) in (1+1) dimensions. This DQCP occurs in an unusual setting, namely at the edge of a (2+1) dimensional bosonic symmetry protected topological phase (SPT) with $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. The DQCP describes a transition between two gapped edges that break different $\mathbb{Z}_2$ subgroups of the full $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. Our construction is based on an exact mapping between the SPT edge theory and a $\mathbb{Z}_4$ spin chain. This mapping reveals that DQCPs in this system are directly related to ordinary $\mathbb{Z}_4$ symmetry breaking critical points.