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Exploring the Koch fractal lattice with quantum renormalization group method

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  • Joyia, Wajid
  • Khan, Salman
  • Khan, Khalid
  • Khan, Mahtab Ahmad

Abstract

We investigate quantum criticality of many-body systems in the context of dimensions through the behavior of tripartite entanglement and tripartite quantum coherence. Following the approach of quantum renormalization group (QRG) method, the analysis on one-dimensional Heisenberg Ising model and non-integer Hausdorff dimensional Koch fractal lattice is made with the increasing size of the systems and anisotropy in the spin components. In thermodynamics limit, the two quantities develop three different regions for each system, signaling the existence of two critical points. The presence of quantum criticality is supported by the divergence of the first derivative of both quantities and their scaling with the increasing number of particles. Our study shows that quantum criticality in the non-integer Hausdorff dimension of Koch fractal lattice is more sensitive to the size than in the one-dimensional spin chains.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:593:y:2022:i:c:s0378437122000565
    DOI: 10.1016/j.physa.2022.126948
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    References listed on IDEAS

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    1. 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.
    2. Jafari, R. & Langari, A., 2006. "Second order quantum renormalisation group of XXZ chain with next-nearest neighbour interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 213-222.
    3. 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.
    4. X. Xiao & Z. Chen & Z. Liu & H. Li & W. Nie & C. Zhang & G. Zhou, 2014. "Spin-filtering and charge- and spin-switching effects in a quantum wire with periodically attached stubs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-6, January.
    5. A. Osterloh & Luigi Amico & G. Falci & Rosario Fazio, 2002. "Scaling of entanglement close to a quantum phase transition," Nature, Nature, vol. 416(6881), pages 608-610, April.
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