Aron Beekman   ベークマン アーロン


Scientist / Scientific software developer

location : Tokyo, Japan


My publications on: arXivInspireGoogle ScholarResearcherIDORCID

on this page: HighlightsPublicationsPopular PhD thesisMSc thesis

other pages: CV


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My publications on: arXivInspireGoogle ScholarResearcherIDORCID


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 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) — 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 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 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 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)

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