Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup

Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. We study, as a concrete example, an emergent ℤ₂-gauged system with global symmetry U⁡(1), namely, the ℤ₂-gauged Bose-Hubbard model both in 1D and in 2D. In certain limits, there is an emergent mixed 't Hooft anomaly between the quotient U⁡(1) symmetry and the dual ℤ₂ symmetry. In 1D, the superfluid phase is mapped to an intrinsically gapless symmetry-protected topological (SPT) phase, as supported by density-matrix renormalization group (DMRG) calculations. In 2D, the original superfluid-insulator transition becomes a generalized deconfined quantum critical point (DQCP) between a gapless SPT phase, where an SPT order coexists with Goldstone modes, and a U⁡(1)-symmetry-enriched topological (SET) phase. We also discuss the stability of these phases and the critical points to small perturbations and their potential experimental realizations.

Based on https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.245108