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Condensed Matter > Strongly Correlated Electrons
Title: Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
(Submitted on 3 Mar 2023 (v1), last revised 18 Sep 2023 (this version, v3))
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 \textit{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 (CLS) 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.
Submission history
From: Gerardo Naumis [view email][v1] Fri, 3 Mar 2023 18:10:13 GMT (4879kb,D)
[v2] Wed, 22 Mar 2023 16:56:13 GMT (2441kb,D)
[v3] Mon, 18 Sep 2023 19:23:16 GMT (896kb,D)
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