Energy gap responsible for the 1/3 magnetization plateau in spin-1/2 trimerized chain

The magnetization process and elementary excitation spectra of the spin-1/2 trimerized quantum Heisenberg chain are investigated by means of Green's function theory combined with Jordan-Wigner transformation. At zero temperature, a 1/3 magnetization plateau of the system is observed. Meanwhile, we obtain the ground state phase diagram, in which the Luttinger liquid phase, the magnetization plateau state, the gapless phase and the ferromagnetic state are revealed. At finite temperatures, the magnetization behaves differently, implying the system lies in different states under different magnetic fields. It is shown that the elementary excitation spectra can unpuzzle the magnetization process. It is also found that the energy gap in the spectra is responsible for the observed 1/3 magnetization plateau.