Abstract
The band structure of some translationally invariant lattice Hamiltonians contains strictly dispersionless flat bands (FB). These are induced by destructive interference and typically host compact localized eigenstates (CLS) which occupy a finite number of unit cells. FBs are important due to macroscopic degeneracy and consequently due to their high sensitivity and strong response to different types of weak perturbations. We use a recently introduced classification of FB networks based on CLS properties, and extend the FB Hamiltonian generator introduced in Phys. Rev. B 95, 115135 (2017) to an arbitrary number of bands in the band structure, and arbitrary size of a CLS. The FB Hamiltonian is a solution to equations that we identify with an inverse eigenvalue problem. These can be solved only numerically in general. By imposing additional constraints, e.g., a chiral symmetry, we are able to find analytical solutions to the inverse eigenvalue problem.
- Received 25 October 2018
- Corrected 31 March 2021
DOI:https://doi.org/10.1103/PhysRevB.99.125129
©2019 American Physical Society
Physics Subject Headings (PhySH)
Corrections
31 March 2021
Correction: A minor typographical error in an inline equation in the fourth sentence of the fourth paragraph in Sec. IV has been fixed.