Chiral ordered phases in a frustrated S=1 chain with uniaxial   single-ion-type anisotropy
  The ground-state phase transitions of a frustrated S=1 Heisenberg chain with the uniaxial single-ion-type anisotropy and the frustrating next-nearest-neighbor coupling are studied. For the system, it has been shown that there are gapless and gapped chiral phases in which the chirality \kappa_l = S^x_l S^y_{l+1} - S^y_l S^x_{l+1} exhibits a finite long-range order (LRO) and the spin correlation decays either algebraically or exponentially. In this study, the transitions between the Haldane and chiral phase and between the large-D (LD) and chiral phase are investigated using the infinite-system density-matrix renormalization group method. It is found that there exist two types of gapped chiral phases, "chiral Haldane" and "chiral LD" phases, in which the string LRO coexists with the chiral LRO and the string correlation decays exponentially, respectively. 
Toshiya Hikihara