Unusual critical points between atomic insulating phases

Abstract: We study a class of quantum phase transitions between featureless bosonic atomic insulators in $(2+1)$ dimensions, where each phase exhibits neither topological order nor protected edge modes. Despite their lack of topology, these insulators may be ``obstructed'' in the sense that their Wannier centers are not pinned to the physical atomic sites. These insulators represent distinct phases, as no symmetry-preserving adiabatic path connects them. Surprisingly, we find that the critical point between these insulators can host a conformally invariant state described by quantum electrodynamics in $(2+1)$ dimensions (QED$_3$). The emergent electrodynamics at the critical point can be stabilized if the embedding of the microscopic lattice symmetries suppresses the proliferation of monopoles, suggesting that even transitions between trivial phases can harbor rich and unexpected physics. We analyze the mechanism behind this phenomenon, discuss its stability against perturbations, and explore the embedding of lattice symmetries into the continuum through anomaly matching. In all the models we analyze, we confirm that the QED$_3$ is indeed emergeable, in the sense that it is realizable from a local lattice Hamiltonian.