Information driven renormalisation group on irregular lattices

Traditionally, real-space renormalisation group (RSRG) is performed by applying a single, often heuristic, coarse-graining transformation to blocks of identical nature across the system. In the absence of such translation invariance, the coarse-graining transformations should be adapted to different regions. This inherent difficulty made it elusive to develop a model-independent paradigm for RSRG in inhomogeneous systems. In this work we address this gap by extending the recent information-theoretical formulation of RSRG to arbitrary irregular lattices. To showcase our method, we tackle the problem of dimer coverings on quasiperiodic Ammann-Beenker tilings. The coarse-graining rules, computed numerically using real-space mutual information neural estimation, (1) vary depending on the location of the block and (2) map the degrees of freedom into emergent "super-dimers" obeying an effective exclusion constraint at the larger-scale. This result indicates an intriguing discrete scale-invariance and proximity of the original model to an RG fixed point.