Skip to main content
SpringerLink
Log in

Entanglement entropy in extended quantum systems

  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of freedom in different regions of space. Close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. In the second part I consider the unitary time evolution of such systems following a ‘quantum quench’ in which a parameter in the Hamiltonian is suddenly changed, and argue that finite regions should effectively thermalise at late times, after interesting transient effects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Calabrese, J. Cardy, J. Stat. Mech. 0406, P06002 (2004)

    Article  Google Scholar 

  2. P. Calabrese, J. Cardy, J. Stat. Mech. 0504, P04010 (2005)

    Article  MathSciNet  Google Scholar 

  3. P. Calabrese, J. Cardy, Phys. Rev. Lett. 96, 136801 (2006); P. Calabrese, J. Cardy, J. Stat. Mech. 0706, P008 (2007)

    Article  ADS  Google Scholar 

  4. L. Amico, R. Fazio, A. Osterloh, V. Vedral, to appear in Rev. Mod. Phys.; e-print arXiv:quant-ph/0703044

  5. C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  6. C. Holzhey, F. Larsen, F. Wilczek, Nucl. Phys. B 424, 44 (1994)

    Article  MathSciNet  Google Scholar 

  7. G. Refael, J.E. Moore, Phys. Rev. Lett. 93, 260602 (2001)

    Article  MathSciNet  Google Scholar 

  8. V. Korepin, Phys. Rev. Lett. 92, 096402 (2004)

    Article  ADS  Google Scholar 

  9. I. Peschel, J. Stat. Mech. 0412, P12005 (2004)

    Article  Google Scholar 

  10. J. Cardy, O. Castro-Alvaredo, B. Doyon, to appear in J. Stat. Phys., e-print arXiv:0706.3384

  11. M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac, e-print arXiv:0704.3906

  12. E. Barouch, B. McCoy, Phys. Rev. A 2, 1075 (1970); E. Barouch, B. McCoy, Phys. Rev. A 3, 786 (1971); E. Barouch, B. McCoy, Phys. Rev. A 3, 2137 (1971)

    Article  ADS  Google Scholar 

  13. K. Sengupta, S. Powell, S. Sachdev, Phys. Rev. A 69, 053616 (2004)

    Article  ADS  Google Scholar 

  14. V. Eisler, I. Peschel, J. Stat. Mech. 0706, P06005 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rudolph Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK

    J. L. Cardya

  2. All Souls College, Oxford, UK

    J. L. Cardya

Authors
  1. J. L. Cardya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. L. Cardya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cardya, J.L. Entanglement entropy in extended quantum systems. Eur. Phys. J. B 64, 321–326 (2008). https://doi.org/10.1140/epjb/e2008-00102-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2008-00102-5

PACS

Search

Navigation