Fig. 2: Numerical results of finite hyperbolic clusters with PBCs and partially OBCs.
From: Hyperbolic band topology with non-trivial second Chern numbers
a, b The eigen-spectra of hyperbolic abelian clusters under PBCs, and the mass terms are (m = 0.7, a = 0.2) and (m = 0.7, a = 3.2). The blue circle and red dots correspond to numerical results obtained by the direct diagonalization and U(1) hyperbolic band theory, respectively. c, d The spatial profiles of eigenmodes (marked by blue and orange arrows in Fig. 2a, b) for the topological hyperbolic clusters under PBCs with mass term being (m = 0.7, a = 0.2) and (m = 0.7, a = 3.2), respectively. e, f The eigen-spectra of hyperbolic abelian clusters under partially OBCs, and the mass terms are (m = 0.7, a = 0.2) and (m = 0.7, a = 3.2), respectively. The colormap corresponds to the quantity \(V(\varepsilon )\). g, h The spatial profiles of eigenmodes (marked by red and green arrows in Fig. 2e, f) for the topological hyperbolic clusters with partial OBCs, and the mass terms are (m = 0.7, a = 0.2) and (m = 0.7, a = 3.2), respectively. Orange and blue shaded regions correspond to non-trivial and trivial bandgaps, respectively.
