Exactly Solvable Model for a Deconfined Quantum Critical Point in 1D
Carolyn Zhang, Michael Levin
Abstract
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 (SPT) phase with ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry. The DQCP describes a transition between two gapped edges that break different ${\mathbb{Z}}_{2}$ subgroups of the full ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ 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.