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

Understand

The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and $U(1)$ charge conservation are both preserved.

• In this paper, we generalize the Lieb-Schultz-Mattis theorem to systems with higher-form symmetries, which act on extended objects of dimension $n > 0$.
• The prototypical lattice system with higher-form symmetry is the pure abelian lattice gauge theory whose action consists only of the field strength.
• We first construct the higher-form generalization of the Lieb-Schultz-Mattis theorem with a proof.