Renormalization group study of electromagnetic interaction in multi-Dirac-node systems

We theoretically study the electromagnetic interaction in Dirac systems with N nodes by using the renormalization group, which is relevant to the quantum critical phenomena of topological phase transition (N = 1) and Weyl semimetals (N = 4 or N = 12). Compared with the previous work for N = 1 [H. Isobe and N. Nagaosa, Phys. Rev. B 86, 165127 (2012)], we obtained the analytic solution for the large N limit, which differs qualitatively for the scaling of the speed of light c and that of electron v; i.e., v does not change while c is reduced to v. We also found a reasonably accurate approximate analytic solution for generic N, which well interpolates between N = 1 and large N limit, and it concludes that c(2)v(N) is almost unrenormalized. The temperature dependence of the physical properties, the dielectric constant, magnetic susceptibility, spectral function, DC conductivity, and mass gap are discussed based on these results.