Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • News & Views
  • Published:


Tensors cast their nets for quarks

Many aspects of gauge theories — such as the one underlying quantum chromodynamics, which describes quark physics — evade common numerical methods. Tensor networks are getting closer to a solution, having successfully tackled the related problem of a three-dimensional quantum link model.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Tensor network states.


  1. Magnifico, G. et al. Nat. Commun. 12, 3600 (2021).

    Article  ADS  Google Scholar 

  2. Wilson, K. G. Phys. Rev. D 10, 2445–2459 (1974).

    Article  ADS  Google Scholar 

  3. Aoki, S. et al. Eur. Phys. J. C 80, 113 (2020).

    Article  ADS  Google Scholar 

  4. Troyer, M. & Wiese, U.-J. Phys. Rev. Lett. 94, 170201 (2005).

    Article  ADS  Google Scholar 

  5. Orús, R. Ann. Phys. 349, 117–158 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  6. Bañuls, M. C. & Cichy, K. Rep. Prog. Phys. 83, 024401 (2020).

    Article  ADS  Google Scholar 

  7. Felser, T. et al. Phys. Rev. X 10, 041040 (2020).

    Google Scholar 

  8. Robaina, D., Bañuls, M. C. & Cirac, J. I. Phys. Rev. Lett. 126, 050401 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  9. Chandrasekharan, S. & Wiese, U.-J. Nucl. Phys. B 492, 455–471 (1997).

    Article  ADS  Google Scholar 

  10. Bañuls, M. C. et al. Eur. Phys. J. D 74, 165 (2020).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Mari Carmen Bañuls or Krzysztof Cichy.

Ethics declarations

Competing interests

The authors declare no competing interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bañuls, M.C., Cichy, K. Tensors cast their nets for quarks. Nat. Phys. 17, 762–763 (2021).

Download citation

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing