  We study the magnetization plateau at a third of the saturation magnetization
of the S=1/2 trimerized XXZ spin chain at T=0. The appearance of the plateau
depends on the values of the XXZ anisotropy and the magnitude of the
trimerization. This plateauful-plateauless transition is a quantum phase
transition of the Berezinskii-Kosterlitz-Thouless type, which is difficult to
precisely detect from the numerical data. To determine the phase boundary line
of this transition precisely, we use the level crossing of low-lying
excitations obtained from the numerical diagonalization. We also discuss the
S=1/2 ferromagnetic-ferromagnetic-antiferromagnetic chain.
