Metal-insulator transition in infinitesimally weakly disordered flat bands

We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence (d + 1) local unitary transformations parametrized angles ${\theta}_i$. Without loss generality, we consider case two separated finite gap $\Delta$. perturbed states originating described an effective tight binding network with on- and off-diagonal strength which depends manifold original W is only affecting overall scale Hamiltonian. Upon variation for d = 1 2 find that localization persists any choice unitaries, length can be maximized specific values Instead, in 3 identify non-perturbative metal-insulator transition upon varying angles.