Title: Fubini–Study metric and topological properties of flat band electronic states: the case of an atomic chain with s − p orbitals
Abstract: Abstract The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with s − p orbitals are explored. This model is mapped onto a Kitaev–Creutz type model, providing a useful framework to understand the topology through a nontrivial winding number and the geometry introduced by the Fubini–Study (FS) metric. This metric allows us to distinguish between pure states of systems with the same topology and thus provides a suitable tool for obtaining the fingerprint of flat bands. Moreover, it provides an appealing geometrical picture for describing flat bands as it can be associated with a local conformal transformation over circles in a complex plane. In addition, the presented model allows us to relate the topology with the formation of compact localized states and pseudo-Bogoliubov modes. Also, the properties of the squared Hamiltonian are investigated in order to provide a better understanding of the localization properties and the spectrum. The presented model is equivalent to two coupled SSH chains under a change of basis.