A novel intermediate phase in S=2 antiferromagnetic chains with uniaxial anisotropy

We study ground state properties of the $S=2$ quantum antiferromagnetic chain with a uniaxially anisotropic Hamiltonian: $H = \sum_{j} [S_{j} \cdot S_{j+1} + D (S^{z}_{j})^2 ]$ by a Monte Carlo calculation. While it has been reported that a string order parameter vanishes exponentially at the isotropic Heisenberg point ($D=0$), we found it tends to remain finite in the thermodynamic limit around $D=1.2$. This implies that the model for $S=2$ has a novel intermediate phase between the Haldane phase and the large-$D$ phase, as was anticipated from the earlier argument based on the Valence-Bond-Solid picture.