Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models

Abstract

The authors construct a Lieb-Schultz-Mattis (LSM)-type theorem applicable for abelian gauge theories without matter. This theorem is based on generalized global symmetries acting on Wilson lines. It provides strong constraints on possible phases, realized in lattice gauge theories. The generalized LSM theorem is demonstrated on the example of a U(1) gauge theory that simulates the quantum dimer model on a bipartite lattice. The authors find a mixed `t Hooft anomaly involving the generalized global symmetry at the Rokhsar-Kivelson critical point that corresponds to the LSM constraint.