Figure 4: Gap versus band geometry for the kagomé lattice model.
(a) Gap and geometry data for the kagomé lattice model with NN-only hoppings, as a function of the only coupling ratio λ1/t1. (b) The same data as a one-dimensional submanifold in band geometry space, which we parameterize in terms of Berry curvature fluctuations σB and the averaged trace condition 
. The upper set (larger gap Δ) of points are gaps for the N=8 bosonic Laughlin state at v=1/2, while the lower are for the bosonic Moore–Read state at v=1. (c) Gap for the kagomé lattice model with both nearest-neighbour and next-nearest-neighbour couplings, as a function of band-geometric parameters (σB, 
) for the Laughlin state of N=8 bosons at v=1/2. (d) Gap as a function of (σB, 
) for the Moore–Read state of N=10 bosons at v=1, for the same coupling values.
