Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies

Using mainly numerical methods, we investigate the ground-state phase diagram of the S=2 quantum spin chain described by $H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + ΔS_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $Δ$ denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the case with $Δ\ge 0$ and $D \ge 0$ for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the $Δ$-$D$ plane consists of four phases; the XY 1 phase, the Haldane/large-$D$ phase, the intermediate-$D$ phase and the Néel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-$D$ state belong to the same phase; (2) there exists the intermediate-$D$ phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the $Δ$-$D$ plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-$D$ phase.

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