Dynamic mass generation on two-dimensional electronic hyperbolic lattices

The authors show here that two-dimensional hyperbolic lattices can be classified as Dirac liquids, Fermi liquids, and flat bands, respectively, featuring vanishing, constant, and diverging density of states near half-filling. On such curved quantum crystals, on-site Hubbard and nearest-neighbor Coulomb repulsion stabilize antiferromagnetic and charge density wave ground states, respectively. The requisite critical couplings for these orderings decrease with the increasing curvature in hyperbolic Dirac fluids, suggesting a curvature-induced weak-coupling quantum phase transitions therein. By contrast, these two orderings develop even for infinitesimal interactions in Fermi liquids and flat-band systems.