Defining 2-group symmetries on lattices and extracting their anomalies

arXiv:2610.37745v1 Announce Type: new Abstract: Ordinary $0$-form symmetries $G$ can mix with $1$-form symmetries $\Pi_2$ to form a $2$-group $\mathcal{G}$. We give a concrete lattice definition for a class of finite $2$-group symmetries in terms of local relations among symmetry operators. These relations identify the Postnikov class $[\rho]\in H^3(BG,\Pi_2)$ that characterizes the mixing. We develop a method to extract anomalies of these symmetries in one spatial dimension by restricting symmetry operations to an interval and comparing their composition near its endpoints. We also construct explicit qubit symmetry actions in $d=1,2,3$ spatial dimensions for a $2$-group with $G=\Pi_2=\mathbb{Z}_2$.