Emergence of Long Period Antiferromagnetic Orders from Haldane Phase in S=1 Heisenberg Chains with D-Modulation

The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Neel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Neel orders. The investigation of the model with longer period D-modulation also confirms this picture.