2025/12/04 by Christopher A. Leong, Leong, Christopher A., Daniel J. Salib +3
Physics and Astronomy · #Topological Materials and Phenomena #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2512.05109
Within the framework of the canonical nearest-neighbor tight-binding model for spinless fermions, a family of two-dimensional bipartite hyperbolic lattices hosts massless Diraclike excitations near half-filling with the iconic vanishing density of states (DOS) near zero energy. We show that a collection of such ballistic quasiparticles remains stable against sufficiently weak pointlike charge impurities, a feature captured by the vanishing average [ρa(0)] and typical [ρt(0)] DOS at zero energy, computed by employing the kernel polynomial method in sufficiently large \ 10, 3\ hyperbolic lattices (Schläfli symbol) with more than 108 and 105 sites, respectively, with open boundary conditions. However, at moderate disorder the system enters a metallic state via a continuous quantum phase transition where both ρa(0) and ρt(0) become finite. With increasing strength of disorder, ultimately an Anderson insulator sets in, where only ρt(0) → 0. The resulting phase diagram for dirty Dirac fermions living on a hyperbolic space solely stems from the background negative spatial curvature, as confirmed from the vanishing ρt(0) for arbitrarily weak disorder on honeycomb lattices, fostering relativistic fermions on a flatland, as the thermodynamic limit is approached.