Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913303090954240 |
|---|---|
| author | Espinosa-Champo, Abdiel Naumis, Gerardo G. |
| author_facet | Espinosa-Champo, Abdiel Naumis, Gerardo G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02126 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals Espinosa-Champo, Abdiel Naumis, Gerardo G. Strongly Correlated Electrons Mesoscale and Nanoscale Physics 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. |
| title | Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2303.02126 |