In a fermionic quantum vacuum, the parameters kμ of a CPT-violating Chern–Simons-like action term induced by CPT-violating parameters of the fermionic sector depend on the universality class of the system. As a concrete example, we consider the Dirac Hamiltonian of a massive fermionic quasiparticle and add a particular term with purely-spacelike CPT-violating parameters bμ = (0, b). A quantum phase transition separates two phases, one with a fully-gapped fermion spectrum and the other with topologically-protected Fermi points (gap nodes). The emergent Chern–Simons "vector" kμ = (0, k) now consists of two parts. The regular part, k reg , is an analytic function of |b| across the quantum phase transition and may be nonzero due to explicit CPT violation at the fundamental level. The anomalous (nonanalytic) part, k anom , comes solely from the Fermi points and is proportional to their splitting. In the context of condensed-matter physics, the quantum phase transition may occur in the region of the BEC–BCS crossover for Cooper pairing in the p-wave channel. For elementary particle physics, the splitting of Fermi points may lead to neutrino oscillations, even if the total electromagnetic Chern–Simons-like term cancels out.
Dynamics of a quantum phase transition in the Aubry-André-Harper model with
p
-wave superconductivity
