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Magnetoelectric effect of the spin-1/2 Heisenberg-Ising ladder in a presenceof the external electric and magnetic fields is rigorously examined by takinginto account Katsura-Nagaosa-Balatsky mechanism. It is shown that the appliedelectric field may control a quantum phase transition between the N\'eel(stripy) ordered phase and the disordered paramagnetic phase. The staggeredmagnetization vanishes according to a power law with the Ising-type criticalexponent 1/8, the electric polarization exhibits a weak singularity and thedielectric susceptibility shows a logarithmic divergence at this particularquantum phase transition. The external electric field may alternatively invokea discontinuous phase transition accompanied with abrupt jumps of thedielectric polarization and susceptibility on assumption that the externalmagnetic field becomes nonzero.

Enhanced magnetoelectric effect near a field-driven zero-temperature quantum phase transition of the spin-1/2 Heisenberg-Ising ladder