  Multi-Weyl semimetals are new types of Weyl semimetals which have anisotropic
non-linear energy dispersion and a topological charge larger than one, thus
exhibiting a unique quantum response. Using a unified lattice model, we
calculate the optical conductivity numerically in the multi-Weyl semimetal
phase and in its neighboring gapped states, and obtain the characteristic
frequency dependence of each phase analytically using a low-energy continuum
model. The frequency dependence of longitudinal and transverse optical
conductivities obeys scaling relations that are derived from the winding number
of the parent multi-Weyl semimetal phase and can be used to distinguish these
electronic states of matter.
