# Dr Pieter Naaijkens

Lecturer

- naaijkensp@cardiff.ac.uk
- +44 (0)29 2087 4522
- Room M/2.09, 21-23 Senghennydd Road, Cathays, Cardiff, CF24 4AG

## Overview

#### Research interests

I am interested in quantum spin systems and their applications to quantum information theory, with a focus on the use of functional analysis and operator algebraic techniques. I primarily study of quantum spin systems with topological order, and how one can obtain a full understanding of the (quasi)particle excitations of such systems. The properties of these excitations can be described by tensor categories, and a substantial part of my work is related to how one can obtain this tensor category by studying certain representations of the *C ^{*}*-algebra of quasi-local observables. An important question we have been working on recently is how stable this structure is with respect to perturbations of the underlying dynamics defining the system, which also is relevant in the classification of topological phases. I have also been working on applying some operator-algebraic techniques to study quantum information.

#### Research group

I am a member of the GAPT (Geometry, Algebra, Mathematical Physics and Topology) Research Group. There also is a GAPT seminar.

## Biography

### Qualifications

- PhD, Radboud University Nijmegen (2012)
- MSc in Mathematics, Utrecht University (2007)
- MSc in Theoretical Physics, Utrecht University (2007)

### Honours and awards

- Annales Henri Poincaré Prize (2016)
- Marie Skłodowska-Curie Individual Fellowship (2015-2018)
- NWO Rubicon Fellowship (2012-2013)

### Academic positions

- 2020 - present: Lecturer, Cardiff University
- Nov 2018 - 2019: Postdoc, Universidad Complutense de Madrid
- Sep 2017- Oct 2018: Marie Skłodowska-Curie fellow (return), RTWH Aachen University
- Sep 2015 - Aug 2017: Marie Skłodowska-Curie fellow (outgoing), University of California, Davis
- Apr 2012 - Aug 2015: Postdoc, Leibniz University Hannover
- Jun 2012 - Jun 2014: NWO Rubicon fellow, Leibniz University Hannover
- Oct 2007 - Jan 2012: PhD candidate, Radboud University Nijmegen

### Committees and reviewing

- School of Mathematics Digital Learning Group

## Publications

### 2020

- Cha, M., Naaijkens, P. and Nachtergaele, B. 2020. On the stability of charges in infinite quantum spin systems. Communications in Mathematical Physics 373, pp. 219-264. (10.1007/s00220-019-03630-1)
- Kato, K. and Naaijkens, P. 2020. An entropic invariant for 2D gapped quantum phases. Journal of Physics A: Mathematical and Theoretical 53(8), article number: 85302. (10.1088/1751-8121/ab63a5)

### 2018

- Cha, M., Naaijkens, P. and Nachtergaele, B. 2018. The complete set of infinite volume ground states for Kitaev's abelian quantum double models. Communications in Mathematical Physics 357(1), pp. 125-157. (10.1007/s00220-017-2989-4)

### 2017

- Fiedler, L., Naaijkens, P. and Osborne, T. J. 2017. Jones index, secret sharing and total quantum dimension. New Journal of Physics 19(2), article number: 23039. (10.1088/1367-2630/aa5c0c)

### 2016

- Bachmann, S., Dybalski, W. and Naaijkens, P. 2016. Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems. Annales Henri Poincaré 17, pp. 1737-1791. (10.1007/s00023-015-0440-y)

### 2015

- Naaijkens, P. and Fiedler, L. 2015. Haag duality for Kitaev's quantum double model for abelian groups. Reviews in Mathematical Physics 27(9), article number: 1550021. (10.1142/S0129055X1550021X)
- Chang, L.et al. 2015. On enriching the Levin-Wen model with symmetry. Journal of Physics A: Mathematical and Theoretical 48(12), pp. 12FT01. (10.1088/1751-8113/48/12/12FT01)
- Naaijkens, P. 2015. Kitaev's quantum double model from a local quantum physics point of view. In: Brunetti, R. et al. eds. Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies, pp. 365-395., (10.1007/978-3-319-21353-8_9)

### 2013

- Naaijkens, P. 2013. Kosaki-Longo index and classification of charges in 2D quantum spin models. Journal of Mathematical Physics 54(8), pp. 81901. (10.1063/1.4818272)

### 2012

- Naaijkens, P. 2012. Haag duality and the distal split property for cones in the toric code. Letters in Mathematical Physics 101(3), pp. 341. (10.1007/s11005-012-0572-7)

### 2011

- Naaijkens, P. 2011. Localized endomorphisms in Kitaev's toric code on the plane. Reviews in Mathematical Physics 23(4), pp. 347. (10.1142/S0129055X1100431X)
- Naaijkens, P. 2011. On the extension of stringlike localised sectors in 2+1 dimensions. Communications in Mathematical Physics 303(2), pp. 385. (10.1007/s00220-011-1200-6)

### 2010

- Naaijkens, P. 2010. Topologische kwantumcomputers: rekenen met vlechten. Nieuw Archief voor Wiskunde 11, pp. 187-193.

### 2008

- Berdichevsky, L. and Naaijkens, P. 2008. Four-point functions of different-weight operators in the AdS/CFT correspondence. Journal of High Energy Physics 801, pp. -.

## Teaching

#### Teaching

In the spring semester I will be teaching the following modules:

- MA2003 Complex Analysis (2020/21)
- MA4016 Quantum Information (2020/21)

Previously I have taught the following modules:

- MA2003 Complex Analysis (2019/20)

#### Previous teaching

Before I moved to Cardiff, I taught:

- Spring 2018: Quantum Information (with David DiVincenzo) (Aachen)
- Spring 2016: MAT 22A (Linear Algebra) (Davis)
- Summer 2014: teaching assistant Lie-Algebren und ihre Darstellungen in der Physik (Hannover)
- Summer 2013: Quantum Spin Systems on Infinite Lattices. Lecture notes can be found here (Hannover)
- Fall 2012: teaching assistant Ergänzungen zur klassischen Physik (Hannover)
- Spring 2011: teaching assistant Symmetry Breaking (Nijmegen)
- Spring 2010: teaching assistant Inleiding Fourieranalyse (Nijmegen)
- Fall 2009: teaching assistant Topologie (Nijmegen)
- Spring 2009: teaching assistant bachelor course Introduction to partial differential equations (Nijmegen)
- Spring 2008: teaching assistant for Analysis I (Nijmegen)

## Supervision

#### EPSRC studentship (position has been filled)

We are currently taking applications for an EPSRC funded doctoral studentship with project title *Operator Algebraic Methods in Topological Phases and Quantum Information*, with application deadline **16 March 2020**. The project will be co-supervised with Gandalf Lechner. The main goal is to use operator algebraic methods to describe physical quantum systems with infinitely many degrees of freedom, with a focus on applications to some combination of the following topics:

- gapped 2D topological quantum phases
- superselection sectors
- anyons / braid statistics
- quantum information theory
- quantum spin systems
- subfactors

More information about the vacancy can be found on the FindAPhD website, or contact me if you have any questions about the project.

### Past projects

- Leander Fiedler, PhD. Co-supervision with Reinhard Werner. Leibniz University Hannover (Jan 2017)
- Deniz Stiegemann, MSc. Co-supervision with Tobias Osbore. Leibniz University Hannover (Oct 2015)