Weak higher form symmetry breaking and decodabiilty transitions in mixed state topological orders

Understanding topologically ordered states in open quantum systems is both conceptually and practically important in the intersection of condensed matter and quantum information science. In this presentation, we consider topologically ordered mixed states through the lens of spontaneous symmetry breaking (SSB) tied to higher-form symmetry. In particular, we show how the decodability transition of topological order, when the state is under local decoherence, can be related to an SSB transition of a weak 1-form symmetry. By the standard Kramers-Wannier duality, this transition is also dual a transition between a traditional SSB and a strong-to-weak SSB phases of a 0-form symmetry.