Dynamic mass generation on two-dimensional correlated quantum hyperbolic fluids

Free electrons hopping on hyperbolic lattices, constructed by periodically tilling regular p-gon with q nearest-neighbor sites on a curved space of negative curvature can harbor a variety of emergent band structures. In particular, for even p, they can be grouped into three broad categories: (a) hyperbolic Fermi liquids, (b) hyperbolic Dirac liquids and (c) hyperbolic flat bands, respectively accommodating constant, vanishing and divergent density of states near the half-filling. Irrespective of these microscopic details, from numerical self-consistent Hartree-Fock analyses we show that the nearest-neighbor (V₁) and on-site (U) Coulomb repulsions respectively gives rise to charge-density-wave and antiferromagnet orders featuring staggered pattern of average electronic density and magnetization in all these systems. Both quantum orders open a mass gap near the charge neutrality point. While these orderings take place for infinitesimal strength of Coulomb interactions in hyperbolic Fermi liquid and flat bands, on hyperbolic Dirac materials such orderings take place beyond critical couplings via a quantum phase transition. We also present the scaling behavior of such mass gaps with interaction strengths, as well as showcase their spatial variations.