IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v593y2022ics0378437122000565.html
   My bibliography  Save this article

Exploring the Koch fractal lattice with quantum renormalization group method

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122000565
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.126948?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mzaouali, Zakaria & El Baz, Morad, 2019. "Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 119-130.
    2. Wang, Yimin & Su, Yang & Liu, Maoxin & You, Wen-Long, 2020. "Entanglement measures in the quantum Rabi model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    3. Ferenc Iglói & Csaba Zoltán Király, 2024. "Entanglement detection in postquench nonequilibrium states: thermal Gibbs vs. generalized Gibbs ensemble," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-12, June.
    4. 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.
    5. Zheng, Yi-Dan & Mao, Zhu & Zhou, Bin, 2022. "Optimal dense coding and quantum phase transition in Ising-XXZ diamond chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    6. Mohammad Pouranvari, 2023. "Characterizing the delocalized–localized Anderson phase transition based on the system’s response to boundary conditions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(4), pages 1-7, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:593:y:2022:i:c:s0378437122000565. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.