Electronic instabilities in Penrose quasicrystals: Competition, coexistence, and collaboration of order

Quasicrystals lack translational symmetry, but can still exhibit long-range order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group approach to the prototypical quasicrystalline Penrose tiling Hubbard model treating competing electronic instabilities in an unbiased, beyond-mean-field fashion. Our work reveals a delicate interplay between charge and spin degrees of freedom in quasicrystals. Depending on the range of interactions and hopping amplitudes, we unveil a rich phase diagram including antiferromagnetic orderings, charge density waves, and subleading, superconducting pairing tendencies. For certain parameter regimes, we find a competition of phases, which is also common in crystals, but additionally encounter phases coexisting in a spatially separated fashion and ordering tendencies which mutually collaborate to enhance their strength. We therefore establish that quasicrystalline structures open up a route towards this rich ordering behavior uncommon to crystals and that an unbiased, beyond-mean-field approach is essential to describe this physics of quasicrystals correctly