A parent model for symmetry-protected topological phases, topological order, and symmetry breaking in (2+1)d

Exploring the rich landscape of interacting topological phases and their phase transitions is an important open problem. In this talk, we introduce a (2+1)d lattice model that serves as a versatile parent theory for symmetry-protected topological phases protected by both ordinary global symmetries and one-form global symmetries. This model further captures exotic phases with both symmetry-enriched topological order and spontaneous symmetry breaking. By analyzing dualities, anomalies, and boundary states in this theory, we illustrate its utility as a simple platform for studying the interplay of zero-form and one-form symmetries in topological states.