Localised Pair Formation in Bosonic Flat-Band Hubbard Models

Using a generalised version of Gershgorin's circle theorem, rigorous boundaries on the energies lowest states broad class line graphs above critical filling are derived for hardcore bosonic systems. Also lower boundary energy gap towards next is established. Additionally, it shown that corresponding eigenstates dominated by subspace spanned containing compactly localised pair and overlap as well. Overall, this strongly suggests formationin ground rigorously proves some in it, including inhomogeneous chequerboard chain well two novel examples regular dimensional graphs.