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Quantum polarization effects associated with the conformal anomaly in astatic magnetic field background may generate a transverse electric current inthe vacuum. The current may be produced either in an unbounded curved spacetimeor in a flat spacetime in a physically bounded system. In both cases, themagnitude of the electric current is proportional to the beta-functionassociated with renormalization of the electric charge. In our article, weinvestigate the electric current density induced by the magnetic field in thevicinity of a Dirichlet boundary in the scalar QED. Using first-principlelattice simulations we show that the electric current, generated by this`conformal magnetic effect at the edge' (CMEE), is well described by theconformal anomaly provided the conformal symmetry is classically unbroken.Outside of the conformal limit, the current density is characterized by ananomalous power law near the edge of the system and by an exponentialsuppression of the current far away from the edge.

Conformal magnetic effect at the edge: a numerical study in scalar QED