Machine-learning RG transformations on a 2d quasicrystal

Machine Learning (ML) is an increasingly valuable tool for the study of condensed matter physics. However, despite many successes, applications where ML conceptually drives theoretical research are scarce. Here we set ML the harder task of providing insight into a problem for which there is very little understanding. Dimer models, one of the oldest problems in statistical physics, were recently introduced to Ammann Beenker tilings. The model showed unexpected features such as long-ranged anisotropic non-monotonic dimer-dimer correlations. A deeper understanding of their origin remains elusive.

To elucidate these results we worked co-operatively with ML, using a combined analytical and numerical approach incorporating the recently developed Mutual Information Renormalization Group (RG) scheme. Remarkably, ML identifies that the statistics can be expressed in terms of emergent large-scale 'super-dimers'. The result reveals an emergent scale invariance, demonstrating proximity to an RG fixed point understood as the same dimer problem re-appearing at a coarse-grained level. Our findings provide a rare example of successfully applying RG to a 2D quasicrystal model, and portray a new approach for discovering coarse-grained representations in complex systems.