Multipolar phase in frustrated spin-1/2 and spin-1 chains

The J1-J2 spin-chain model with nearest-neighbor J1 and next-nearest-neighbor antiferromagnetic J2 interaction is one of the most popular frustratedmagnetic models. This model system has been extensively studied theoretically and applied to explain the magnetic properties of the real low-dimensional materials. However, the existence of different phases for the J1-J2 model in an axial magnetic field h is either not understood or has been controversial. In this paper, we show the existence of higher order p > 4 multipolar phase near the critical point (J2/J1) c = -0.25. The criterion to detect the quadrupolar or spin nematic (SN)/spin density wave of type two ( SDW2) phase using the inelastic neutron scattering (INS) experiment data is also discussed, and INS data of LiCuVO4 compound is modeled. We discuss the dimerized and degenerate ground state in the quadrupolar phase. The major contribution of binding energy in the spin-1/2 system comes from the longitudinal component of the nearest-neighbor bonds. We also study spin nematic/SDW2 phase in spin-1 system in large J2/J1 limit.