Gauging spatial symmetries and the classification of topological crystalline phases

Understand

We put the theory of interacting topological crystalline phases on a systematic footing.

• These are topological phases protected by space-group symmetries.
• Our central tool is an elucidation of what it means to "gauge" such symmetries.
• We introduce the notion of a "crystalline topological liquid", and argue that most (and perhaps all) phases of interest are likely to satisfy this criterion.