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

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Using mainly numerical methods, we investigate the ground-state phase diagram of the S = 2 quantum spin chain described by \mathcal{H} = \sum_{j}(S_{j}^{x}S_{j+1}^{x} + S_{j}^{y}S_{j+1}^{y} + \Delta S_{j}^{z}S_{j+1}^{z}) + D \sum_{j}(S_{j}^{z})^{2}, where \Delta denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. We restrict ourselves to the case of \Delta\geq 0 and D\geq 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 \Delta--D plane consists of four phases; the XY1 phase, the Haldane/large-D phase, the intermediate-D phase, and the Néel phase. The remarkable natures of the phase diagram are as follows: (1) there exists an intermediate-D phase which was predicted by Oshikawa in 1992; (2) the Haldane state and the large-D state belong to the same phase; (3) the shape of the phase diagram on the \Delta--D plane is different from that considered so far. We note that this is the first report on the observation of the intermediate-D phase.
2011-04-15