Phase diagram of the easy-plane ferromagnetic-antiferromagnetic S=1 Heisenberg chain

We perform a systematic investigation on the ground state of the easy-plane S=1 spin model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using the Density Matrix Renormalization Group (DMRG) method. By analyzing the chirality order parameter, the spin correlation function and the spin structure factor, we determine the phase diagram. A chiral phase is identified in an intermediate frustration region even when the anisotropic value Δ is small. In addition, the spin-fluid phase with power-law decaying correlation exists for the anisotropic case when the frustration strength α is small. When α is large, the ground state is of the short-range-ordered incommensurate phase.