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Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice

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  • Xu, Yu-Liang
  • Kong, Xiang-Mu
  • Liu, Zhong-Qiang
  • Wang, Chun-Yang

Abstract

The quantum entanglement and quantum phase transition of the transverse-field Ising model on a two-dimensional square lattice were investigated by applying the quantum renormalization group method. The quantum critical point (QCP) and the correlation length exponent, ν, were obtained. By taking the concurrence as a measure of entanglement, the entanglement between spin blocks near the QCP is calculated as the size of the system becomes large. The entanglement reaches a maximum close to QCP, and can exist in a small range around QCP just at the limit of thermodynamics. The nonanalytic behavior of the derivative of the entanglement with the external field shows that the system undergoes a second order quantum phase transition from a ferromagnetic phase to a paramagnetic phase. The finite-size scaling behavior of the entanglement is described, and the relationship between the entanglement exponent, θ, the correlation length exponent, ν, and the dimension of the system d is also found, i.e., θ=1/(νd).

Suggested Citation

  • Xu, Yu-Liang & Kong, Xiang-Mu & Liu, Zhong-Qiang & Wang, Chun-Yang, 2016. "Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 217-223.
    • Handle: RePEc:eee:phsmap:v:446:y:2016:i:c:p:217-223
    DOI: 10.1016/j.physa.2015.12.002
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    References listed on IDEAS

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    1. Gao, Kun & Xu, Yu-Liang & Kong, Xiang-Mu & Liu, Zhong-Qiang, 2015. "Thermal quantum correlations and quantum phase transitions in Ising-XXZ diamond chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 10-16.
    2. Solano-Carrillo, E. & Franco, R. & Silva-Valencia, J., 2011. "Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2208-2214.
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    Cited by:

    1. Joyia, Wajid & Khan, Salman & Khan, Khalid & Khan, Mahtab Ahmad, 2022. "Exploring the Koch fractal lattice with quantum renormalization group method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).

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