12:30 pm MCP - 3rd Floor Atrium
What's inside a parameterized family?
The Thouless charge pump, the Berry-Chern number of a spin in a magnetic field, and their recent generalizations to higher dimensions are important examples of parameterized topological families of gapped ground states. One way to realize such families is by spontaneously breaking a continuous G symmetry down to a subgroup H. The resulting Goldstone modes can carry topological terms, and if we further gap out the Goldstone modes, we get a parameterized family. Our main result is that the possible families are constrained by the anomaly of the original G symmetric state, with the full structure given by a 'compatibility relation'. Separately, I will discuss examples of topological families from classical physics, and their potential usefulness in understanding phase transitions.