Since April 2012 I am a postdoc at the Institut für Theoretische Physik of the Leibniz Universität Hannover, in the Quantum Information Group. I am supported by a NWO Rubicon grant. Before I was a PhD student of Michael Müger and Klaas Landsman, in the mathematical physics group at Radboud University Nijmegen. My PhD thesis can be found below.

Contact details

Pieter Naaijkens, picture taken by Leander Fiedler

Pieter Naaijkens
Leibniz Universität Hannover
Institut für Theoretische Physik
Appelstraße 2
30167 Hannover
E-mail:pieter.naaijkens AT ..hostname..
(please replace ..hostname.. by

If you want to contact me by signed or encrypted mail: my GnuPG key ID is #B5A5E651.


I am interested in the mathematical intricacies of topologically ordered systems. In particular, I try to use the tools and techniques of operator algebra, algebraic quantum field theory and tensor categories in this setting. For example, one can study the properties of the excitations of such systems by mimicking the Doplicher-Haag-Roberts theory of superselection sectors, a toolkit in algebraic quantum field theory, in the setting of topologically ordered spin systems. It turns out that this works very well: one can recover for example all excitations and their fusion rules and statistics for the toric code in this setting. This algebraic approach also appears to be very fruitful to study, e.g., the classification of topological phases


Articles and preprints

  1. Kitaev's quantum double model from a local quantum physics point of view
    To appear in R. Brunetti C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds), Advances in Algebraic Quantum Field Theory (Springer), 2015 (preprint)
  2. On Enriching the Levin-Wen model with Symmetry (with L. Chang, M. Cheng, S.X. Cui, Y. Hu, W. Jin, R. Movassagh, Z. Wang, A. Young)
    J. Phys. A: Math. Theor. 48:12FT01, 2015 (journal | preprint)
  3. Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems (with S. Bachmann and W. Dybalski), 2014 (preprint)
  4. Haag duality for Kitaev's quantum double model for abelian groups (with L. Fiedler), 2014 (preprint)
  5. Quantum spin systems on infinite lattices
    Lecture notes for a one-semester course given at Leibniz Universität, 2013 (preprint)
  6. Kosaki-Longo index and classification of charges in 2D quantum spin models
    J. Math. Phys. 54:081901-1–17, 2013 (journal | preprint)
  7. Haag duality and the distal split property for cones in the toric code
    Lett. Math. Phys. 101:341–354, 2012 (journal | preprint)
  8. Localized endomorphisms in Kitaev's toric code on the plane
    Rev. Math. Phys. 23:347–373, 2011 (journal | preprint)
  9. On the extension of stringlike localised sectors in 2+1 dimensions
    Comm. Math. Phys. 303:385–420, 2011 (journal | preprint)
  10. Topologische kwantumcomputers: rekenen met vlechten
    Nieuw Arch. Wiskd. 11:187–193, sept. 2010, semi-popular, in Dutch (journal)
  11. Four-point functions of different-weight operators in the AdS/CFT correspondence (with L. Berdichevsky)
    JHEP 0801:071, 2008 (journal | preprint)


  1. Anyons in infinite quantum systems: QFT in d=2+1 and the toric code, PhD Thesis, Radboud University, 2012 (Defended May 15) (download)
  2. Four-point functions of N=4 SYM4 in the AdS/CFT correspondence, Master's Thesis, Utrecht University, 2007
  3. Cartesisch gesloten deelcategoriëen van Top, Bachelor's Thesis, Utrecht University, 2004

Please contact me if you would like a hardcopy version of my PhD thesis.


Here you can find a selection of my talks.


I am currently not teaching any course. Before I have taught in the following courses:

In August 2008, I gave a summer course (see here for information for participants) for high-school students who do not have the right prerequisites for admission to the mathematics bachelor program.

I also participated in the Sprint-Up program summer 2008 till summer 2010.


I will attend the following conferences and workshops:

Past events

From September 2008 until June 2011, I organised the PhD colloquium in Nijmegen.


Some interesting weblogs and websites: