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arXiv:2412.00739

Quantum entanglement entropy and Tomonaga-Luttinger liquid to liquid transition in biquadratic spin-1 XY chain with rhombic single-ion anisotropy

Yanwei Dai, Su Yao, Sam Young Cho, Huan-Qiang Zhou

Published Dec 1, 2024• 0 citations
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Abstract

Quantum phase transitions (QPTs) are investigated in biquadratic spin-$1$ XY chain with rhombic single-ion anisotropy by using the ground state energy (GE), the bipartite entanglement entropy (BEE), and the mutual information (MI). It turns out that there are three spin nematic phases and two Tomonaga-Luttinger (TL) liquid phases with the central charge $c = 1$. The TL Liquid phases emerge roughly for biquadratic interaction strength two times stronger than the absolute value of the single-ion anisotropy. The GE and the derivatives up to the second order reveal a first-order QPT between spin nematic ferroquarupole (FQ) phases but cannot capture an evident signal of QPTs between the spin nematic phases and the TL Liquid phases as well as QPT between the two TL liquid phases. The TL liquid-to-liquid transition point features a highly degenerate state and the spin-block entanglement entropy increases logarithmically with block size. The BEE exhibits a divergent or convergent behavior identifying the TL Liquid or spin nematic FQ phases, respectively. Similarly, the MI and the spin-spin correlation are shown to decay algebraically or exponentially with increasing the lattice distance in the TL Liquid or spin nematic FQ phases, respectively. In the TL liquid phase, the exponents $η_I$ and $η_z$ of the MI and the spin-spin correlation vary with the interaction parameter of the biquadratic interaction strength and the rhombic single-ion anisotropy and satisfy the relationship of $η_z <η_I$. Such changes of characteristic behavior of the BEE, the MI and the spin-spin correlation indicate an occurrence of the Berezinskii-Kosterlitz-Thouless (BKT)-type QPT between the TL Liquid phase and the spin nematic FQ phase. The staggered spin fluctuation $\langle S^x S^y \rangle$ is shown to play a significant role for the emergence of the TL liquid phase and thus give rise to the BKT-type QPT.

DOI
10.48550/arxiv.2412.00739

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Quantum phase transitions (QPTs) are investigated in biquadratic spin-111 XY chain with rhombic single-ion anisotropy by using the ground state energy (GE), the bipartite entanglement entropy (BEE), and the mutual information (MI). It turns out that there are three spin nematic phases and two Tomonaga-Luttinger (TL) liquid phases with the central charge c=1c = 1c=1. The TL Liquid phases emerge roughly for biquadratic interaction strength two times stronger than the absolute value of the single-ion anisotropy. The GE and the derivatives up to the second order reveal a first-order QPT between spin nematic ferroquarupole (FQ) phases but cannot capture an evident signal of QPTs between the spin nematic phases and the TL Liquid phases as well as QPT between the two TL liquid phases. The TL liquid-to-liquid transition point features a highly degenerate state and the spin-block entanglement entropy increases logarithmically with block size. The BEE exhibits a divergent or convergent behavior identifying the TL Liquid or spin nematic FQ phases, respectively. Similarly, the MI and the spin-spin correlation are shown to decay algebraically or exponentially with increasing the lattice distance in the TL Liquid or spin nematic FQ phases, respectively. In the TL liquid phase, the exponents ηIη_IηI​ and ηzη_zηz​ of the MI and the spin-spin correlation vary with the interaction parameter of the biquadratic interaction strength and the rhombic single-ion anisotropy and satisfy the relationship of ηz<ηIη_z <η_Iηz​<ηI​. Such changes of characteristic behavior of the BEE, the MI and the spin-spin correlation indicate an occurrence of the Berezinskii-Kosterlitz-Thouless (BKT)-type QPT between the TL Liquid phase and the spin nematic FQ phase. The staggered spin fluctuation ⟨SxSy⟩\langle S^x S^y \rangle⟨SxSy⟩ is shown to play a significant role for the emergence of the TL liquid phase and thus give rise to the BKT-type QPT.
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