Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry

We elucidate how the presence of higher-form symmetries affects the dynamics of thermalization in isolated quantum systems. Under reasonable assumptions, we analytically show that a $p$-form symmetry in a $(d+1)$-dimensional quantum field theory leads to the breakdown of the eigenstate thermalization hypothesis for many nontrivial $(d-p)$-dimensional observables. For higher-form (i.e., $p\geq 1$) symmetry, this indicates the absence of thermalization for observables that are non-local but much smaller than the whole system size. We numerically demonstrate this argument for the (2+1)-dimensional $\mathbb{Z}_2$ lattice gauge theory. While local observables such as the plaquette operator thermalize, the non-local observable exciting a magnetic dipole instead relaxes to the generalized Gibbs ensemble that takes account of the $\mathbb{Z}_2$ 1-form symmetry.