Ground State Phase Diagrams of Frustrated Spin-S XXZ Chains: Chiral   Ordered Phases
  The ground-state phase diagram of the frustrated spin-S XXZ chain with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied numerically by using the density-matrix renormalization-group method for the cases of S = 1/2, 3/2, and 2. We are paricularly interested in the possible gapless and gapped chiral phases, in which the chirality \kappa_l = S_l^x S_{l+1}^y - S_l^y S_{l+1}^x exhibits a finite long-range order whereas the spin correlation decays either algebraically or exponentially. We show that the gapless chiral phase appears in a broad region of the phase diagram for general S. By contrast, the gapped chiral phase is found for integer S in a narrow region of the phase diagram, while it has not been identified for half-odd integer S within our numerical accuracy. By combining the results with our previous result for S = 1, we discuss the S-dependence of the phase diagram. The prediction from a bosonization analysis on the decay exponent of the spin correlation is verified. 
T. Hikihara, M. Kaburagi, H. Kawamura