Theory of Twist Liquids: Gauging an Anyonic Symmetry

Understand

Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures.

• Twist defects are static point-like objects that permute the labels of orbiting anyons.
• Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids, which are generically non-Abelian.
• We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions.