  The competition between quantum and classical magnetization plateaus of S=1/2
frustrated Heisenberg chains with modified exchange couplings is investigated.
The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a
3-fold degenerate udu-type classical plateau at 1/3 of the saturation
magnetization accompanied by the spontaneous Z_3 translational symmetry
breakdown. The stability of this plateau phase against period 3 exchange
modulation which favors the 00u-type quantum plateau state (00= singlet dimer)
is studied by bosonization, renormalization group and numerical diagonalization
methods. The ground state phase diagram and the spin configuration in each
phase are numerically determined. The translationally invariant Valence Bond
Solid-type model with 4-spin and third neighbor interactions, which has the
exact 00u-type quantum plateau state, is also presented. The phase transition
to the classical udu-type ground state is also observed by varying the strength
of 4-spin and third neighbor interactions. The relation between these two types
of models with quantum plateau states is discussed.
