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Journal of Applied Mathematics and Physics

Quantum Phase Transition for One-Dimensional Spin-1 XXZ Model with Uniaxial Single-Ion-Type Anisotropy

Chunhuan Xiang, Honglei Wang

Published Jan 1, 2019• 0 citations
Publisher

Abstract

The quantum phase transitions for one-dimensional spin-1 XXZ model with uniaxial single-ion-type anisotropy are investigated by numerical simulation. The Gaussion transition occurred between the Larged-D phase and Neel phase, which is a gapped phase. The results of ground state energy, local order parameter and entanglement entropy agree with each other. The figures for all of the physical observable are shown in the text.

DOI
10.4236/jamp.2019.77102

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We explore numerically the inverse participation ratios in the ground state of one-dimensional spin-1 XXZXXZXXZ chains with the rhombic single-ion anisotropy. By employing the techniques of density-matrix renormalization group, effects of the rhombic single-ion anisotropy on various information theoretical measures are investigated, such as the fidelity susceptibility, the quantum coherence, and the entanglement entropy. Their relations with the quantum phase transitions are also analyzed. The phase transitions from the YYY-N\'eel phase to the large-Ex{E}_{x}Ex​ or the Haldane phase can be well characterized by the fidelity susceptibility. The second-order derivative of the ground-state energy indicates all the transitions are of second order. We also find that the quantum coherence, the entanglement entropy, the Schmidt gap, and the inverse participation ratios can be used to detect the critical points of quantum phase transitions. Results drawn from these quantum information observables agree well with each other. Finally we provide a ground-state phase diagram as functions of the exchange anisotropy $\mathrm{\ensuremath{\Delta}}$ and the rhombic single-ion anisotropy EEE.
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