Magnetization plateau and quantum phase transition of the S=1/2 trimerized XXZ spin chain

We study the plateau of the magnetization curve at $M = M_{\rm s}/3$ ($M_{\rm s}$ is the saturation magnetization) of the $S=1/2$ trimerized $XXZ$ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the $\Delta-t$ plane, where $\Delta$ denotes the $XXZ$ anisotropy and $t$ the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.