Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries

Understand

We investigate the gauging of higher-form finite Abelian symmetries and their sub-groups in quantum spin models in spatial dimensions $d=2$ and 3.

• Doing so, we naturally uncover gauged models with dual higher-group symmetries and potential mixed 't Hooft anomalies.
• We demonstrate that the mixed anomalies manifest as the symmetry fractionalization of higher-form symmetries participating in the mixed anomaly.
• Gauging is realized as an isomorphism or duality between the bond algebras that generate the space of quantum spin models with the dual generalized symmetry structures.