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Scaling of entanglement close to a quantum phase transition

Author

Listed:
  • A. Osterloh

    (Dipartimento di Metodologie Fisiche e Chimiche (DMFCI)
    NEST-INFM)

  • Luigi Amico

    (Dipartimento di Metodologie Fisiche e Chimiche (DMFCI)
    NEST-INFM)

  • G. Falci

    (Dipartimento di Metodologie Fisiche e Chimiche (DMFCI)
    NEST-INFM)

  • Rosario Fazio

    (NEST-INFM
    Scuola Normale Superiore)

Abstract

Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order1. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant2, and are driven by quantum fluctuations. Examples include transitions in quantum Hall systems3, localization in Si-MOSFETs (metal oxide silicon field-effect transistors; ref. 4) and the superconductor–insulator transition in two-dimensional systems5,6. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement, is the resource that enables quantum computation and communication8. The role of entanglement at a phase transition is not captured by statistical mechanics—a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory9. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.

Suggested Citation

  • 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.
    • Handle: RePEc:nat:nature:v:416:y:2002:i:6881:d:10.1038_416608a
    DOI: 10.1038/416608a
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    Cited by:

    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. 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.
    3. 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.
    4. 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).
    5. 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).
    6. 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).

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