Ground-state properties of the one-dimensional antiferromagnetic chain with frustrated side spins

The properties of the one-dimensional antiferromagnetic chain with frustrated side spins are studied by means of the spin wave theory, the exact diagonalization method and the density matrix renormalization group method. The results show that the Lieb-Mattis type ferrimagnetic state is always the ground state when α<αc1. The system undergoes a first-order phase transition accompanied by a spontaneous symmetry breaking and its acoustic excitation spectrum softens completely near k=0 at the critical point αc1. In the intermediate parameter region αc1<α<αc2, the ground state is a nonmagnetic state called dimer-tetramer state with a small spin gap. A gapped-gapless Berezinskii-Kosterlitz-Thouless phase transition occurs at another critical point αc2 beyond which the nonmagnetic dimer-monomer state becomes the ground state. The value of the critical point αc2 can be precisely determined not only by the level-spectroscopy method, but also the method based on comparing the magnitude of the two types of correlation functions and the method of a scaling analysis of the gap.