Understanding deconfined quantum critical points from crystalline categorical Landau paradigm

Abstract: Deconfined quantum critical points (DQCPs) involving lattice symmetries evade the conventional Landau paradigm because the competing orders break incompatible internal and crystalline symmetries. We show that a class of DQCPs can nevertheless be understood as Landau-type transitions after gauging anomalous onsite symmetries. For spin chains with Lieb-Schultz-Mattis (LSM) anomalies, gauging produces a noninvertible lattice translation whose fusion closes only up to ordinary translations, giving rise to a crystalline categorical symmetry. In the gauged description, the original DQCP becomes a transition between different symmetry breaking patterns of this categorical symmetry. We demonstrate this mechanism in microscopic lattice models; the magnetic-valence-bond-solid (VBS) DQCP realizes a Rep($D_8$)-type crystalline categorical Landau transition, whereas a y-antiferromagnetic-VBS DQCP realizes a Rep($H_8$)-type one. Although Rep($D_8$) and Rep($H_8$) share the same fusion rules, they have inequivalent $F$-symbols and therefore define distinct categorical descriptions. Our results show that the universal categorical structure underlying these DQCPs is encoded in the full fusion category, rather than in the fusion ring alone.