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Xiamen-Cardiff Seminar

Dimer models on quasicrystals

Speaker: Felix Flicker (Cardiff University)
Date: Friday 12 November 2021
Time: 9:30 in UK
Venue: Zoom

Dimer models on quasicrystals How many ways are there of tiling a chess board with dominoes? This is an example of a classical dimer model. Removing one domino reveals the two squares it covered: one black, one white. These can be thought of as a particle-antiparticle pair. Further domino re-arrangements allow the particles to move around on the board. Dimer models provide a general setting to study physical systems in which strong correlations emerge from local constraints. Examples include emergent magnetic monopoles in the spin ice materials, spin liquids, and resonating valence bond states. Despite the simplicity of dimer models they exhibit a range of exotic phenomena, including fractionalisation and topological order. A central question is whether the emergent quasiparticles -- black and white squares in the chess board analogy -- can become deconfined, separating to arbitrary distance at finite energy cost. The answer depends on the symmetries, or otherwise, of the dimer configurations. Dimer models have a long history, with many exact results proven in both finite, and infinite periodic, settings. In this talk I will outline exact results in a new setting: infinite aperiodic tilings based on two-dimensional 'quasicrystals'. Focussing on the Ammann-Beenker tiling, with an 8-fold rotational symmetry and discrete scale invariance, I provide evidence of quasiparticle deconfinement. This is seemingly at odds with the received wisdom that deconfined phases cannot exist in 2+1D compact U(1) gauge theories. I will outline our understanding of how that result likely survives. The behaviour emerges from a rich set of dimer correlations which exhibit a natural scale invariance.

[1] F. Flicker, S. H. Simon, and S. A. Parameswaran, Classical dimers on Penrose tilings, Physical Review X 10, 011005 (2020)
[2] J. Lloyd, S. Biswas, S. H. Simon, S. A. Parameswaran, and F. Flicker, Statistical mechanics of dimers on quasiperiodic tilings, arXiv: 2103.01235

Biography: He is a Lecturer in Physics at Cardiff University, based part-time in Bristol University's Maths department. His interests lie in the application of geometry and topology to condensed matter systems. He previously held the Astor Junior Research Fellowship at New College, Oxford, and a Lindemann Trust Fellowship of the English Speaking Union, which sent him to the University of California, Berkeley. He completed his PhD at the University of Bristol (2011-2015), under the supervision of Jasper van Wezel at the University of Amsterdam. He was on the Perimeter Institute's Perimeter Scholars International programme (2010-2011), where he was supervised by Michel Gingras at the University of Waterloo. He was an undergraduate at St. Catherine's College, Oxford (2005-2010).

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