  We investigate the quantum phase transition in the alternating XY chain with
the XZX+YZY type of three-spin interactions. We present the exact solution
derived by means of the Jordan-Wigner transformation and study the average
magnetization, spin correlations, and von Neumann entropy to establish the
phase diagram. The phase diagram consists of the ferromagnetic phases, the
paramagnetic phases, and the phase with weak magnetization (WM). By examining
the nearest-neighbor transverse spin correlation, we probe that in the WM
phase, the spins within a supercell generate a cluster with a small total spin,
but between the nearest-neighbor supercells are distributed randomly.
Especially for the dimerized limit case, the spins within a supercell tend to
point to opposite directions of the transverse field. In addition, we also
investigate the influence of the three-site interaction, and find that the WM
phase is absent as the strength of the three-site interaction increases. Our
findings shed light on the complex behavior of the alternating XY chain and
provide valuable insights for future studies.
