Plateau of the magnetization curve of the S=1/2 ferromagnetic-ferromagnetic-antiferromagnetic spin chain

I analytically study the plateau of the magnetization curve at M/M(S) = 1/3 (where M(S) is the saturation magnetization) of the one-dimensional S = 1/2 trimerized Heisenberg spin system with ferromagnetic (J(F))-ferromagnetic (J(F))-antiferromagnetic (J(A)) interactions at T = 0. I use the bosonization technique for the fermion representation of the spin Hamiltonian through the Jordan-Wigner transformation. The plateau appears when gamma = J(F)/J(A) < gamma(C), and vanishes when gamma > gamma(C), where the critical value gamma(C) is estimated as gamma(C) = 5 similar to 6. The behavior of the width of the plateau near gamma(C) is of the Kosterlitz-Thouless type. The present theory well explains the numerical result by Hida.