Boundary Deconfined Quantum Criticality at Transitions Between Symmetry-Protected Topological Chains

Decades of research have revealed a deep understanding of topological quantummatter with protected edge modes. We report that even richer physics emergeswhen tuning between two topological phases of matter whose respective edgemodes are incompatible. The frustration at the edge leads to novel boundaryphysics, such as symmetry-breaking phases with exotic non-Landau transitions –even when the edge is zero-dimensional. As a minimal case study we considerspin chains with ℤ_3 ×ℤ_3 symmetry, exhibiting twonontrivial symmetry-protected topological (SPT) phases. At the bulk 1+1Dcritical transition between these SPT phases, we find two stable 0+1D boundaryphases, each spontaneously breaking one of the ℤ_3 symmetries.Furthermore, we find that a single boundary parameter tunes a non-Landauboundary critical transition between these two phases. This constitutes a 0+1Dversion of an exotic phenomenon driven by charged vortex condensation known asdeconfined quantum criticality. This work highlights the rich unexploredphysics of criticality between nontrivial topological phases and providesinsights into the burgeoning field of gapless topological phases.