Multicriticality of Gapped and Gapless Symmetry-Protected Topological Phases

In the presence of symmetries, a given conformal field theory can have topologically distinct manifestations which cannot be smoothly connected ("gapless SPT"). In this talk, we explore phase transitions between such inequivalent critical theories, i.e. phase transitions of phase transitions. In particular, in the rich setting of spin chains with Z3xZ3 symmetry, we find a multicritical point with central charge c=2 and Lieb-Schultz-Mattis anomaly. It serves as a meeting point in the phase diagram for three topologically distinct gapless c=8/5 theories as well as three distinct gapped SPT phases. A multitude of connections between anomalous symmetries and exotic boundary criticality are explored. This arises from nearest-neighbor two-body interactions, thereby bringing the gapless SPT's of Phys. Rev. B 109, L201112 into a physically-motivated regime.