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The elementary excitation of spin lattice models: The quasiparticles of Gentile statistics

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  • Shen, Yao
  • Zhou, Chi-Chun
  • Chen, Yu-Zhu

Abstract

In this paper, we show that the elementary excitations of interacting spin lattice models, such as the Ising models, the Heisenberg models and the abelian Kitaev anyons, can be regarded as the quasiparticles of Gentile statistics. The advantage of the quasiparticle viewpoint is that eigenvalues and eigenstates of these models can be directly obtained by creating and annihilating Gentile quasiparticles. We provide the eigenstates and eigenvalues of d-dimensional Ising model with periodic boundary conditions. We also provide the eigenvalues of the Heisenberg models, the abelian Kitaev anyons, 2-dimensional and 3-dimensional general spin lattice models. In addition, we point out that one kind of next nearest neighbor interacting models and more general interacting model may correspond to several kinds of quasiparticles of Gentile statistics.

Suggested Citation

  • Shen, Yao & Zhou, Chi-Chun & Chen, Yu-Zhu, 2022. "The elementary excitation of spin lattice models: The quasiparticles of Gentile statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    • Handle: RePEc:eee:phsmap:v:596:y:2022:i:c:s0378437122002060
    DOI: 10.1016/j.physa.2022.127223
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    References listed on IDEAS

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    1. Litinskii, L.B. & Kryzhanovsky, B.V., 2020. "Eigenvalues of Ising connection matrix with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    2. Iakov Karandashev & Boris Kryzhanovsky, 2013. "Increasing the attraction area of the global minimum in the binary optimization problem," Journal of Global Optimization, Springer, vol. 56(3), pages 1167-1185, July.
    3. Dai, Wu-Sheng & Xie, Mi, 2004. "A representation of angular momentum (SU(2)) algebra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 497-504.
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    Cited by:

    1. Shen, Yao & Zhang, Fu-Lin & Chen, Yu-Zhu & Zhou, Chi-Chun, 2023. "Masking quantum information in the Kitaev Abelian anyons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).

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