Ohio State University
In the traditional Landau theory of continuous phase transitions, a symmetry group can break down to any subgroup. Violations of this rule is a hallmark of unconventional quantum phase transitions (QPTs) beyond the Ginzburg-Landau-Wilson paradigm, one example being the deconfined quantum critical point. Here we discuss a family of QPTs between symmetry enriched topological orders driven by anyon condensation, which are beyond the Landau paradigm. We show that some symmetries must be broken if certain anyons condense in a given symmetry enriched topological order, and obtain two rules for these "topology enforced symmetry breakings". We discuss how these rules allow us to predict the symmetry breaking phases in the neighborhood of a symmetry enriched topological order, such as the magnetic orders and valence bond crystals neighboring a quantum spin liquid.