Application of the non-Abelian bosonization to spin-1 ladder and tube in a high magnetic field

We review the non-Abelian bosonization method for one-dimensional spin-1 systems, which was first proposed by Tsvelik. As a new application of it, we discuss field-induced critical phases of spin-1 antiferromagnetic 2-leg ladder and 3-leg tube. It is shown that the ground states in both the ladder and the tube become a one-component Tomonaga-Luttinger liquid when the interchain coupling is weak and the external uniform field is sufficiently larger than the lower critical value.