![Pieter Naaijkens](https://profiles-cardiff.imgix.net/attachments/8706?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Dr Pieter Naaijkens
- Ar gael fel goruchwyliwr ôl-raddedig
Timau a rolau for Pieter Naaijkens
Uwch Ddarlithydd
Trosolwyg
Diddordebau ymchwil
I am interested in quantum spin systems, topological order, and their applications to quantum information theory, with a focus on the use of functional analysis and operator algebraic techniques. One of my focus areas is how one can get a full understanding of the (quasi)particle excitations of topologically ordered quantum spin systems. The properties of these excitations can be described by tensor categories, and a significant part of my work is related to how one can get 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.
Rolau o fewn yr Ysgol
Rwy'n dal y rolau canlynol o fewn yr Ysgol
- Cydlynydd Mathemateg Blwyddyn 2 a Chadeirydd y Bwrdd Arholi
- Cydlynydd Anabledd (Heb ei ddiraddio)
Grŵp ymchwil
Rwy'n aelod o Grŵp Ymchwil GAPT (Geometreg, Algebra, Ffiseg Fathemategol a Topoleg). Mae seminar GAPT hefyd .
Cyhoeddiad
2026
- Benini, M. et al., 2026. C*-categorical prefactorization algebras for superselection sectors and topological order. Communications in Mathematical Physics 407 20. (10.1007/s00220-025-05525-w)
- Bols, A. et al., 2026. The category of anyon sectors for non-abelian quantum double models. Communications in Mathematical Physics 407 2. (10.1007/s00220-025-05492-2)
2025
- Jones, C. et al., 2025. Local topological order and boundary algebras. Forum of Mathematics, Sigma 13 e135. (10.1017/fms.2025.16)
2022
- Naaijkens, P. and Ogata, Y. 2022. The split and approximate split property in 2D systems: stability and absence of superselection sectors. Communications in Mathematical Physics 392 , pp.921-950. (10.1007/s00220-022-04356-3)
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) 085302. (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) 023039. (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 (09) 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., 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.081901. (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 (04), 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 0801 , pp.-.
Adrannau llyfrau
- Naaijkens, P. 2015. Kitaev's quantum double model from a local quantum physics point of view. In: Brunetti, R. et al., Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies , pp.365-395. (10.1007/978-3-319-21353-8_9)
Erthyglau
- Benini, M. et al., 2026. C*-categorical prefactorization algebras for superselection sectors and topological order. Communications in Mathematical Physics 407 20. (10.1007/s00220-025-05525-w)
- Bols, A. et al., 2026. The category of anyon sectors for non-abelian quantum double models. Communications in Mathematical Physics 407 2. (10.1007/s00220-025-05492-2)
- Jones, C. et al., 2025. Local topological order and boundary algebras. Forum of Mathematics, Sigma 13 e135. (10.1017/fms.2025.16)
- Naaijkens, P. and Ogata, Y. 2022. The split and approximate split property in 2D systems: stability and absence of superselection sectors. Communications in Mathematical Physics 392 , pp.921-950. (10.1007/s00220-022-04356-3)
- 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) 085302. (10.1088/1751-8121/ab63a5)
- 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)
- Fiedler, L. , Naaijkens, P. and Osborne, T. J. 2017. Jones index, secret sharing and total quantum dimension. New Journal of Physics 19 (2) 023039. (10.1088/1367-2630/aa5c0c)
- 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)
- Naaijkens, P. and Fiedler, L. 2015. Haag duality for Kitaev's quantum double model for abelian groups. Reviews in Mathematical Physics 27 (09) 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. 2013. Kosaki-Longo index and classification of charges in 2D quantum spin models. Journal of Mathematical Physics 54 (8), pp.081901. (10.1063/1.4818272)
- 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)
- Naaijkens, P. 2011. Localized endomorphisms in Kitaev's toric code on the plane. Reviews in Mathematical Physics 23 (04), 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)
- Naaijkens, P. 2010. Topologische kwantumcomputers: rekenen met vlechten. Nieuw Archief voor Wiskunde 11 , pp.187-193.
- Berdichevsky, L. and Naaijkens, P. 2008. Four-point functions of different-weight operators in the AdS/CFT correspondence. Journal of High Energy Physics 0801 , pp.-.
Ymchwil
Diddordebau ymchwil
Mae gen i ddiddordeb mewn ffiseg mathemategol. Hynny yw, mae'r problemau mathemategol yr wyf yn ymchwilio iddynt yn cael eu cymell gan ffiseg. Mae gen i ddiddordeb arbennig mewn astudio systemau troelli cwantwm gyda threfn topolegol. Mae systemau o'r fath yn arwain at excitations lled-gronynnau unonig ac wedi darparu llawer o enghreifftiau o ffenomenau corfforol newydd a diddorol. Rwy'n canolbwyntio ar yr astudiaeth fathemategol drylwyr o systemau o'r fath gan ddefnyddio dulliau o theori algebra gweithredydd. Dyma rai o'r prosiectau yr wyf yn meddwl amdanynt:
- Sefydlogrwydd y sectorau superselect. Gellir disgrifio'r dyfyniadau anyonic mewn cyfnodau cwantwm gyda chymaledd amrediad hir yn fathemategol gan ddefnyddio categorïau tensor modiwlaidd. Ar ben hynny, disgwylir mai gwrthdroad o'r cyfnod cwantwm wedi'i gapio yw hwn: os ydym yn ymwneud â'r system heb gau'r bwlch ynni, ni ddylai'r strwythur algebraidd hwn newid. Gyda fy nghydweithredwyr rwyf wedi datblygu dull i gael y categori tenor modiwlaidd hwn o egwyddorion cyntaf, o ystyried yr Hamiltonaidd yn unig yn y system. Yn yr enghraifft bwysig o fodelau dwbl cwantwm abelian, gallwn brofi bod y categori un yn cael yn y ffordd honno yn wir yn wrthdrawiad o gam.
- Dadansoddi theori ar gyfer unrhyw un. Mae prosesau gwasgaru yn chwarae rhan allweddol mewn llawer o arbrofion. Felly, mae angen dealltwriaeth ddamcaniaethol dda o brosesau gwasgaru. Gyda fy nghydweithwyr rwyf wedi datblygu fersiwn o theori gwasgaru Haag-Ruelle y gellir ei gymhwyso i systemau troelli cwantwm. Ar hyn o bryd rydym yn gweithio ar ymestyn hyn i gynnwys gwasgaru unrhyw unons.
- Damcaniaeth Gwybodaeth Quantum. Cymhellwyd fy niddordebau mewn trefn topolegol i ddechrau gan geisiadau i gyfrifiadura cwantwm. Y dyddiau hyn, rwy'n gweithio ar yr ochr wybodaeth cwantwm: yn benodol, mae gen i ddiddordeb mewn theori gwybodaeth cwantwm mewn systemau sydd â llawer iawn o ryddid yn ddi-ben-draw, fel theori maes cwantwm. Mewn systemau o'r fath, mae dull algebraidd gweithredwr yn naturiol iawn, ac mae'n ymddangos y gellir cymhwyso rhai technegau theori y sector i dasgau gwybodaeth cwantwm hefyd.
Prosiectau a ariennir
- Ysgoloriaeth PhD, 2020-2024 (EPSRC DTP)
- Cymrodoriaeth Unigol Marie Sklodowska-Curie, 2015-2018 (UE)
- Cymrodoriaeth Rubicon, 2012-2014 (Cyngor Ymchwil yr Iseldiroedd)
Digwyddiadau wedi'u trefnu
- Cyfarfod LQP Rhithwir Cyntaf (Mehefin 2020)
Addysgu
Addysgu
Yn semester y gwanwyn byddaf yn addysgu'r modiwlau canlynol:
- Algebra Llinol II (2026/27)
- Gwybodaeth Cwantwm (2026/27)
Yn flaenorol rwyf wedi dysgu'r modiwlau canlynol:
- Algebra Llinol II (2025/26)
- Algebra Llinol II a Theori Gwybodaeth Cwantwm (2024/25)
- Algebra Llinol II a Theori Gwybodaeth Cwantwm (2023/24)
- Dadansoddiad Cymhleth a Theori Gwybodaeth Cwantwm (2022/23)
- Dadansoddiad Cymhleth a Theori Gwybodaeth Cwantwm (2021/22)
- Dadansoddiad Cymhleth a Theori Gwybodaeth Cwantwm (2020/21)
- Dadansoddiad Cymhleth (2019/20)
Addysgu blaenorol
Cyn i mi symud i Gaerdydd, dysgais:
- Gwanwyn 2018: Quantum Information (gyda David DiVincenzo) (Aachen)
- Gwanwyn 2016: MAT 22A (Algebra Llinol) (Davis)
- Haf 2014: cynorthwyydd addysgu Lie-Algebren und ihre Darstellungen in der Physik (Hannover)
- Haf 2013: Systemau Sbin Cwantwm ar Dellt Anfeidrol. Gellir dod o hyd i nodiadau darlith yma (Hannover)
- Fall 2012: teaching assistant Ergänzungen zur klassischen Physik (Hannover)
- Gwanwyn 2011: cynorthwyydd addysgu Symmetry Breaking (Nijmegen)
- Gwanwyn 2010: cynorthwyydd addysgu Inleiding Fourieranalyse (Nijmegen)
- Fall 2009: cynorthwyydd addysgu Topologie (Nijmegen)
- Gwanwyn 2009: cwrs baglor cynorthwyydd addysgu Cyflwyniad i hafaliadau differol rhannol (Nijmegen)
- Gwanwyn 2008: cynorthwyydd addysgu ar gyfer Dadansoddiad I (Nijmegen)
Bywgraffiad
Cymwysterau
- PhD, Prifysgol Radboud Nijmegen (2012)
- MSc mewn Mathemateg, Prifysgol Utrecht (2007)
- MSc mewn Ffiseg Ddamcaniaethol, Prifysgol Utrecht (2007)
Anrhydeddau a dyfarniadau
- Gwobr Annales Henri Poincaré (2016)
- Cymrodoriaeth Unigol Marie Skłodowska-Curie (2015-2018)
- Cymrodoriaeth Rubicon NWO (2012-2013)
Aelodaethau proffesiynol
Rwy'n aelod o'r cymdeithasau canlynol:
- Cymdeithas Mathemategol Llundain
- Sefydliad Ffiseg
- Cymdeithas Ryngwladol Ffiseg Mathemategol
- Royal Dutch Mathematics Society (KWG)
Safleoedd academaidd blaenorol
- 2026 - presennol: Uwch Ddarlithydd, Prifysgol Caerdydd
- 2020 - 2026: Darlithydd, Prifysgol Caerdydd
- Tachwedd 2018 - 2019: Ôl-ddoethuriaeth, Universidad Complutense de Madrid
- Medi 2017- Hydref 2018: Cymrawd Marie Skłodowska-Curie (dychwelyd), Prifysgol RTWH Aachen
- Medi 2015 - Awst 2017: Cymrawd Marie Skłodowska-Curie (sy'n mynd allan), Prifysgol Califfornia, Davis
- Ebrill 2012 - Awst 2015: Ôl-ddoethuriaeth, Prifysgol Leibniz Hannover
- Meh 2012 - Mehefin 2014: Cymrawd NWO Rubicon, Prifysgol Leibniz Hannover
- Hydref 2007 - Ionawr 2012: Ymgeisydd PhD, Prifysgol Radboud Nijmegen
Pwyllgorau ac adolygu
- Pwyllgor grŵp Ffiseg Mathemategol a Damcaniaethol y Sefydliad Ffiseg (Cadeirydd)
Meysydd goruchwyliaeth
Ar hyn o bryd nid wyf yn hysbysebu unrhyw swyddi a ariennir. Fodd bynnag, rwy'n agored i oruchwylio myfyrwyr PhD hunan-ariannu ar bynciau sy'n gysylltiedig â'm diddordebau ymchwil:
- Damcaniaeth Gwybodaeth Quantum
- Algebras gweithredwr
- Gorchymyn topological & unrhyw un
- Systemau troelli cwantwm
- Categorïau tenor
Cysylltwch â mi am fwy o wybodaeth.
Goruchwyliaeth gyfredol
Prosiectau'r gorffennol
- Mahdie Hamdan, Cyflwr Sylfaen Cyfrol Anfeidrol yn y Model Dwbl Cwantwm nad yw'n Abelian (2024)
Contact Details
[email protected]
+44 29208 74522
Abacws, Ystafell Ystafell 3.67, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
+44 29208 74522
Abacws, Ystafell Ystafell 3.67, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
Themâu ymchwil
Arbenigeddau
- Ffiseg fathemategol
- Quantum llawer o Theori Corff
- Algebras gweithredwr a dadansoddiad swyddogaethol
- Trefn topolegol