Aron Beekman

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Aron Beekman
PhD student with Jan Zaanen from 2006 to 2011

Instituut-Lorentz for Theoretical Physics
Universiteit Leiden
office 234
» visiting address and directions

postal address:
P.O. Box 9506
2300 RA Leiden
The Netherlands

t. +31 71 527 55 30
f. +31 71 527 55 11
e. aron@lorentz.leidenuniv.nl

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Publications

My papers on arXiv

The emergence of gauge invariance: the stay-at-home gauge versus local–global duality J. Zaanen and A.J. Beekman, accepted for Annals of Physics, 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 stay-at-home 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, Frontiers of Physics 6(4):357–369 (2011), arXiv:1106.3946
Even though vortices in type-II 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 relation in a single equation. As an interesting elaboration, we also derive the electrodynamics of two-form sources, where the Maxwell field strength itself obtains a gauge freedom.
Condensing Nielsen-Olesen strings and the vortex-boson 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 Bose-Mott insulator transition, we argue how such a theory must arise. The simple results are directly applicable to other phase transitions.

Posters

Quantum liquid crystals as Hopf-symmetry condensates

Topological order and defect condensation

Supersymmetry as a loophole for the Mermin–Wagner theorem

Gravitons in quantum nematics

Type-II Josephson Junctions

Mini-course on topological interactions

I have given an introduction into the concepts of topological interactions and Hopf symmetry to several people at the Instituut-Lorentz in late January–early February 2006, and a rerun in April.

» More information

PhD Thesis

In my dissertation, I explore the implications of regarding a topological defect line in 3+1 dimesions as a world sheet. From the Goldstone mode in a symmetry-broken state, the dynamics are obtained by a duality transformation, where each world sheet component has a precise physical meaning. Furthermore, the order-to-disorder (quantum) phase transition is now viewed as the proliferation of topological defects, and this well-known vortex–boson duality is generalized to 3+1 dimensions. The highlight result is the prediction of vortex lines of quantized electric current in charged Bose-Mott insulators, with possible relevance to underdoped cuprate superconductors

» Vortex duality in higher dimensions (pdf, 4.4 MB)

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 so-called quantum doubles in 2+1-dimensional 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 image 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 n-gon, 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)