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

This work taps into the idea of gauging finite subgroups of global symmetries in conventional systems to obtain unconventional phases and phase transitions, greatly expanding the conventional Landau paradigm. Assisted by analytical anomaly computations and numerical density-matrix renormalization group calculations, the authors map the ordinary superfluid-insulator transition of the Bose-Hubbard model to novel phase transitions between exotic topological and/or symmetry-breaking phases. The general framework has potential applications in cold atom experiments and digital quantum simulators.