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Cited by 1,472Quantum many-body systemsQuantum Information and CryptographyQuantum Mechanics and Applications

Entanglement in a simple quantum phase transition

Open access
Osborne, Tobias J., Nielsen, Michael A.·2002·Physical Review A
DOI 10.1103/physreva.66.032110
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Abstract

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic $\mathrm{XY}$ model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the $\mathrm{XY}$ model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

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  • Entanglement is expected to play a crucial role in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations at zero temperature.

    “Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations.”

    From Entanglement in Quantum Critical Phenomena (2003) · cites this paper as [12]

  • Osterloh et al. and Osborne and Nielsen found that one- and two-spin entanglement measures in the XY model display a peak either near or at the critical point.

    “Their analysis, focused on single-spin entropies [12] and on two-spin quantum correlations [12,14], suggestively shows that these one-and two-spin entanglement measures display a peak either near or at the critical point.”

    From Entanglement in Quantum Critical Phenomena (2003) · cites this paper as [12]

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Research works printed but not linked: 7

  1. Phys. Rev. A 64 , 042302 (2001), quant-ph/0102137. · arXiv
  2. [32]X. Wang and P. Zanardi (2002), quant-ph/0202108. · arXiv
  3. [34]B. K. Chakrabarti, A. Dutta, and P. Sen, Quantum Ising phases and transitions in transverse Ising models (Springer, Berlin, 1996).
  4. [47]A. Auerbach, Interacting electrons and quantum magnetism (Springer-Verlag, New York, 1994), 1st ed.
  5. [49]A. Osterloh, L. Amico, G. Falci, and R. Fazio (2002), quant-ph/0202029. · arXiv
  6. [51]K. A. Dennison and W. K. Wootters, Phys. Rev. A 65 , 010301 (2001), quant-ph/0106058. · arXiv
  7. [55]W. K. Wootters (2002), quant-ph/0202048. · arXiv

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Authors
Osborne, T. J., & Nielsen, M. A.
Affiliations
The University of Queensland (AU)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2002-09-23
Volume
66
Issue
3
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.66.032110
OpenAlex
W2111145493
Cited by
1,472
References
39
Citations by year
2026: 41 · 2025: 61 · 2024: 54 · 2023: 44 · 2022: 54 · 2021: 53 · 2020: 57 · 2019: 52 · 2018: 55 · 2017: 46 · 2016: 66 · 2015: 58 · 2014: 52 · 2013: 55 · 2012: 58
FWCI
37.79
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum entanglement, quantum phase transitions, transverse-field Ising model, anisotropic XY model, entanglement of formation, critical points, thermal equilibrium, infinite lattices

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