Constrained Models on Quasicrystals

08.06.2023 11:00 – 13:00

Some of the most important phenomena in physics arise when strong correlations emerge from local constraints. Examples include dimer models (tiling a chess board with dominoes) and emergent 'magnetic monopole' excitations in crystals called spin ices. We outline results for a range of constrained models in a new setting: aperiodic Ammann Beenker tilings (AB). These lesser-known cousings of Penrose tilings have the symmetries of certain exotic materials called quasicrystals. We prove the existence of Hamiltonian cycles (visiting each vertex precisely once), and thereby solve a range of related problems including the three-colouring problem and the travelling salesperson problem [1]. Potential applications include adsorption, catalysis, and scanning tunneling microscopy. Using machine learning (RSMI-NE) we identify an emergent discrete scale invariance to the structure of dimer matchings [2,3]. In ongoing work we apply DMRG to the quantum dimer model in this (2D) system.

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Bâtiment: Ecole de Physique

Salle MaNEP

entrée libre