20-06U

The Lagrange multiplier method is used for the investigation of a nonequilibrium steady state with the energy current in the one-dimensional spin-1/2 XX model of a magnetoelectric with the Katsura–Nagaosa–Balatsky mechanism at temperatures close to absolute zero. Within the Jordan–Wigner transformation the Hamiltonian is reduced to a free-fermion form, and can be solved exactly. We construct the phase diagrams and obtain the dependencies of magnetization and electric polarization on the magnetic and electric fields as well as on the energy current and the field, which drives this current.