Magnetic-field control of electric polarization in coupled spin chains with three-site interactions

The linear perturbation renormalization group (LPRG) is used to study coupled X Y chains with Dzyaloshinskii-Moriya (DM) and three-spin interactions in a magnetic field. Starting with a minimal model exhibiting the magnetoelectric effect, a spin-1/2 XY chain with nearest, next-nearest (J(2)(x) ), and DM ( D-1(y)) interactions in a magnetic field, the recursion relations for all effective interactions generated by the LPRG transformation are found. The evaluation of these relations allows us to analyze, among others, the influence of J(2)(x) , D-1(y), three-spin (S-i(x) (Si+1Si+2z)-S-y- S-i(y) S-i+1(x) S-i+2(z)), and interchain interactions on the thermodynamic properties. The field and temperature dependences of the polarization, specific heat, and correlation functions are found. It is shown that an interchain coupling triggers a phase transition indicated by the divergence of the renormalized coupling parameters.