Aron Beekman ベークマン アーロン
recent posts

Nobel Prize in Physics 2016
October 05 2016, 21:54 JST
Yesterday was the announcement of the Nobel Prize in Physics 2016 being awarded to David Thouless, Michael Kosterlitz and Duncan Haldane. Since the topic is very close to my own re… read more »

In Nederland
December 13 2014, 22:13 JST
Update.: om 18.00u in Cafe Goos op de Maasstraat.
Vanochtend ben ik aangekomen in Nederland, ik vlieg terug naar Japan op 1 januari. Tussen werk en vakantie door ben ik maar een… read more »

Skiën in Japan (4): Zao Onsen
May 09 2014, 16:46 JST
Voor het nieuwe jaar had ik twee voornemens: mijn cursus Japanese for Busy People inclusief deel 3 (bedankt Sinterklaas!) afronden en regelmatig schrijven op mijn weblog. Van beide… read more »

Borrel in Amsterdam 1 januari 2014
December 30 2013, 22:36 JST
We zijn voor een paar dagen in Amsterdam op bezoek. Velen van jullie hebben we inmiddels ontmoet, maar bij iedereen langsgaan is helaas niet mogelijk. De dag vóór de terugreis, o… read more »
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Publications –
Popular –
PhD thesis –
MSc thesis
other pages: CV
Publications
My papers on:
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 Dual gauge field theory of quantum liquid crystals in three dimensions
A.J. Beekman, J. Nissinen, K. Wu, J. Zaanen,
arXiv:1703.03157
Combining the results for quantum liquid crystals in two dimensions and vortex–boson duality in three dimensions, we develop the dual theory of the solidtoliquid crystal quantum phase transition in 3+1D. Phonons dualize into twoform gauge fields, and dislocations are string worldsheets with a Burgers vector topological charge. Although this mathematical structure is rather different from vector gauge fields, the phenomenology of the quantum liquid crystal phases is very similar to the situation in two dimensions. Rotational Goldstone modes emerge in any plane with fully restored translational symmetry.
 Dual gauge field theory of quantum liquid crystals in two dimensions
A.J. Beekman, J. Nissinen, K. Wu, K. Liu, R.J. Slager, Z. Nussinov, V. Cvetkovic, J. Zaanen,
Phys. Rep. 683, 1–110 (2017),
arXiv:1603.04254
An extenstive review of using a AbelianHiggs (vortex–boson) type duality to describe dislocationmediated quantum melting of solids into liquid crystals. Phonons are dualized into stress photons: gauge fields mediating stress interactions between dislocations. Upon losing translational rigidity, these stress photons become gapped by the Anderson–Higgs mechanism. Consecutive melting results in a solid → smectic → nematic → superfluid hierarchy. A rotational Goldstone mode emerges in the nematic phase. We also couple in the electromagnetic field, with explicit prediction for optical conductivity, electron loss etc.
 Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
A.J. Beekman,
Ann. Phys. 361, 461–489 (2015),
arXiv:1408.1691
The Heisenberg ferromagnet is a very peculiar system featuring spontaneous symmetry breaking: its classical groundstate unusually is an exact eigenstate of the Hamiltonian. I identify in fact seven special features and show how they are related, and how they can be generalized to other systems using symmetry algebra notions. It turns out one should consider all possible order parameter operators to get a complete picture of the quantum fluctuations and of the lowenergy spectrum.
 Photodrive of magnetic bubbles via magnetoelastic waves
N. Ogawa, W. Koshibae, A.J. Beekman, N. Nagaosa, M. Kubota, M. Kawasaki and Y. Tokura,
PNAS 112(29), 8977–8981 (2015)
My colleague Ogawa manipulates magnetic bubbles by illuminating them with offresonant laser light. He makes them appear, move, extend and coalesce. We were able to give an nice intuitive explanation for these phenomena: the light excites magnetoelastic waves, and those combined elastic–spin waves couple to the domain walls of the bubbles, more strongly at higher curvature.
 Theory of magnonskyrmion scattering in chiral magnets
J. Iwasaki, A.J. Beekman and N. Nagaosa,
Phys. Rev. B 89, 064412 (2014),
arXiv:1309.2361
Studying the elementary process of scattering of magnons by a single skyrmion in chiral magnets, we find strong skewscattering that is wavenumber dependent. In turn the skyrmion moves in the opposite direction. Our analysis shows that the skyrmion acts as a fictious magnetic field on the magnons related to its Berry phase, and that the backaction can be viewed as elastic scattering when taking into account the peculiar, nonNewtonian momentum of the skyrmion.
 Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D
A.J. Beekman, K. Wu, V. Cvetkovic and J. Zaanen,
Phys. Rev. B 88, 024121 (2013),
arXiv:1301.7329
In solids only translational Goldstone modes, phonons, appear even though both translational and rotational symmetry is broken. We show how the rotational modes are confined in the solid and get dynamically deconfined when melting into an isotropic liquid crystal. Surpisingly, in the dual language, the medium for the rotational modes is the condensate of dislocations itself.
 TypeII BoseMott insulators
A.J. Beekman and J. Zaanen,
Phys. Rev. B 86, 125129 (2012) (Editors' suggestion),
arXiv:1207.0286
In typeII superconductors, a magnetic field penetrates in the form of quantized flux lines. Using the duality techniques of "Condensing Nielsen–Olesen strings ...", the BoseMott insulator is a dual superconductor, where now not magnetic field but electric current is expelled by the condensate. Consequently, we predict the existence of a regular lattice of quantized current lines in such systems under externally applied current.
 The emergence of gauge invariance: the stayathome gauge versus local–global duality
J. Zaanen and A.J. Beekman,
Ann Phys 327(4):1146–1161 (2012), arXiv:1108.2791
Whenever there is a conserved current, the conservation law can be explicitly enforced by expressing it as the curl of a gauge field, giving rise to an emergent gauge symmetry. Conversely, in any state where dynamic fluctuations freeze out, there is another emergent gauge symmetry related to local number conservation, called stayathome gauge. We show that these two seemingly separate emerging symmetries are actually two sides of the same coin. This is applied to quantum elasticity, where we find that a relativistic quantum nematic is the realization of linearized gravity.
 Electrodynamics of Abrikosov vortices: the field theoretical formulation
A.J. Beekman and J. Zaanen,
Front. Phys. 6(4):357–369 (2011), arXiv:1106.3946
Even though vortices in typeII superconductors have been known and studied for over 50 years, the electrodynamical phenomena such as dynamic screening and radiation of moving vortices have always been treated as separate individual issues. Using the vortex worldsheet formalism, we can capture all magnetic and electric relations in a single equation. As an interesting elaboration, we also derive the electrodynamics of twoform sources, where the Maxwell field strength itself obtains a gauge freedom.
 Condensing NielsenOlesen strings and the vortexboson duality in 3+1 and higher dimensions
A.J. Beekman, D. Sadri and J. Zaanen,
New. J. Phys. 13:033004 (2011), arXiv:1006.2267
By representing vortices as fluctuating fields, one can describe an order–disorder phase transition as the proliferation of vortices. This was established in 2+1 dimensions by Hagen Kleinert and many others over 20 years ago, because then vortices are exactly like point particles, and can therefore be handled by common quantum field theory techniques. In higher dimensions, the vortices are extened objects, and up to now it was not known how to formalize their collective behaviour. From the known physics of the superfluid to BoseMott insulator transition, we argue how such a theory must arise. The simple results are directly applicable to other phase transitions.
Popular
 (Dutch) Vortexdualiteit
Nederlands Tijdschrift voor Natuurkunde, Dec 2012
PDF (1.0MB)
 (Dutch) 100 jaar supergeleiding
at sargasso.nl
and sciencepalooza.nl
part 1,
part 2
PhD Thesis
In my dissertation at Leiden University under supervision of Jan Zaanen, I explore the implications of regarding a topological defect line in 3+1 dimesions as a world sheet.
From the Goldstone mode in a symmetrybroken state, the dynamics are obtained by a duality transformation, where each world sheet component has
a precise physical meaning. Furthermore, the ordertodisorder (quantum) phase transition is now viewed as the
proliferation of topological defects, and this wellknown vortex–boson duality is generalized to 3+1
dimensions. The highlight result is the prediction of vortex lines of quantized electric current in charged BoseMott
insulators, with possible relevance to underdoped cuprate superconductors
» Vortex duality in higher dimensions (pdf, 4.4 MB)
— also available at Leiden University Library
MSc Thesis
To obtain my Master's degree (Universiteit van Amsterdam, Institute for Theoretical Physics), I looked into the earlier work of my supervisor Sander Bais and some of his PhD students, in which they explored the extension of group symmetry to socalled quantum doubles in 2+1dimensional systems. In this way, the quantum numbers of topological excitations are taken into account as well as those of the regular (gauge) particles. Furthermore, this formalism provides directly for a description of the braid properties of the particles. Such structure can for example arise in gauge theories where the original symmetry is broken down to a finite group.
A next step was to look at the possible condensate phases in such systems; that is, we imagine the new ground state of the system to be one filled with background particles, all represented by a certain state vector of one of the irreducible representations of the symmetry algebra. Because of the braiding with the condensate particles, not every excitation in the new phase can exist freely, and some of them will be ‘confined’.
In my thesis work, I have calculated through almost all possible condensate states in models where the original symmetry is that of an even dihedral group, the symmetry group of a regular ngon, with n even. This leads to a redefinition of the braiding properties of the particles that exist freely in the condensate state. Furthermore, in some condensates the remaining symmetry algebra turns out to be much larger than one would naively expect from just looking at the breaking of the topological and regular parts of the quantum double.
» Quantum double symmetries of the even dihedral groups and their breaking (pdf, 1.0 MB)
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