Spin-1/2 XY chain magnetoelectric: effect of zigzag geometry

A spin-1/2 $XY$ chain model of magnetoelectric on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. By non-uniform spin-rotations the model is reduced to a dimerized $XY$ chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model, zero and finite temperature magnetoelectric effect, obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.