Symmetry-protected flatband condition for Hamiltonians with local symmetry
arXiv:2308.14997 · doi:10.1088/1751-8121/ad909d
Abstract
We derive symmetry-based conditions for tight-binding Hamiltonians with flatbands to have compact localized eigenstates occupying a single unit cell. The conditions are based on unitary operators commuting with the Hamiltonian and associated with local symmetries that guarantee compact localized states and a flatband. We illustrate the conditions for compact localized states and flatbands with simple Hamiltonians with given symmetries. We also apply these results to general cases such as the Hamiltonian with long-range hoppings and higher-dimensional Hamiltonian.
7 pages, 2 figures
References in corpus (11)
- The electronic properties of graphene
- Observation of a localized flat-band state in a photonic Lieb lattice
- Observation of bound states in Lieb photonic lattices
- Flat bands and Wigner crystallization in the honeycomb optical lattice
- Topological Insulators on the Lieb and Perovskite Lattices
- Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
- Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
- Chiral Flat Bands: Existence, Engineering and Stability
- Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry
- Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice
- Isolated flat bands in 2D lattices based on a novel path-exchange symmetry