Symmetric gapped phases: Unconventional critical points and featureless states

Symmetric gapped phases are frequently overlooked in the search for exotic correlated states. However, such phases can arise through nontrivial mechanisms and exhibit unexpected physics. In this talk I will present two connected examples. First, I consider a 1D multiorbital Kondo lattice model in which tuning the kinetic energy of itinerant electrons stabilizes Kondo insulating phases with distinct spin structures. I will present evidence for an unconventional continuous transition between two insulating phases distinguished by their reflection quantum numbers. The critical point falls outside the standard conformal field theory framework, but is consistent with a local quantum critical point picture. Motivated by insights from this 1D setting, I then introduce flat-band spin models in 2D and discuss symmetry constraints. In particular I argue that such models can admit a gapped, unique, and fully symmetric ground state with no signatures of fractionalization. I will conclude by discussing potential realizations in moiré heterostructures.