Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons

Table 1

Symmetry-breaking orders can be probed/defined through linear responses. But topological order cannot be probed/defined through linear responses. We need topological probes to define topological orders.

Order	Experiment
Crystal order	X-ray diffraction
Ferromagnetic order	Magnetization
Antiferromagnetic order	Neutron scattering
Superuid order	Zero viscosity and vorticity quantization
Topological order	Topological degeneracy
(Global dancing pattern)	non-Abelian geometric phase