17-07U

The spin-1/2 XY model of magnetoelectric with the Katsura–Nagaosa–Balatsky mechanism of the coupling between local spins and the electric polarization of the bond connecting these spins on zigzag ladder is considered. Using the Jordan–Wigner transformation, the Hamiltonian is reduced to a free-fermion form, and can be solved exactly. The ground-state phase diagrams are constructed and the magnetic and electric fields dependence of magnetization and electric polarization at zero temperature is calculated.