Chiral magnetic effect at low temperature

We investigate the chiral magnetic effect (CME) under a strong magnetic field B=B₀^x₃ at low temperature TTc^χ. For this purpose, we employ the instanton vacuum configuration with the finite instanton-number fluctuation Δ, which relates to the nontrivial topological charge Qₜ. We compute the vacuum expectation values of the local chiral density ⟨ρ_χ⟩, chiral charge density ⟨n_χ⟩, and induced electromagnetic current ⟨j_μ⟩, which signal the CME, as functions of T and B₀. We observed that the longitudinal electromagnetic current is much larger than the transverse one, |j_⊥/j_∥|~Qₜ, and ⟨n_χ⟩ is equal to |⟨j3,4⟩|. It also turns out that the CME becomes insensitive to the magnetic field as T increases, since the instanton effect decreases. Within our framework, the instanton contribution to the CME becomes almost negligible beyond T≈300 MeV.