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In this talk, we report our recent studies for the chiral magnetic effect,which signals the P- and CP-violations at the heavy ion collisions. We computethe electric current and its correlations, induced by the external magneticfield, inside the hot and dense QCD matter created in the heavy ion collisions.For this purpose, we employ the instanton-liquid model, modified by theHarrington-Shepard caloron at finite T. We observe that the chiral magneticeffect current and its correlations increase with respect to the magneticfield, whereas they decrease as functions of T, due to the diluting instantonensemble. It turns out that the numerical results are in good agreement withthose from the model-independent analyses and lattice QCD simulations. We alsoreproduce the charge separations, observed in the STAR experiment,qualitatively well, considering the simplified Lienard-Wiechert potential,screening and size effects.

QCD under magnetic field: chiral magnetic effect at heavy ion collisions