Field-controlled spin current in frustrated spin chains

We study states with spontaneous spin current, emerging in frustrated antiferromagnetic spin-$S$ chains subject to a strong external magnetic field. As a numerical tool, we use a non-Abelian symmetry realization of the density matrix renormalization group. The field dependence of the order parameter and the critical exponents are presented for zigzag chains with S=1/2, 1, 3/2, and 2.