Symmetry-protected flatband condition for Hamiltonians with local symmetry

TL;DR

This paper establishes symmetry-based criteria for flatband Hamiltonians with local symmetries, enabling the identification of compact localized states in various lattice models.

Contribution

It introduces a novel symmetry-based framework for determining flatbands and compact localized states in Hamiltonians with local symmetries, including complex and higher-dimensional cases.

Findings

Derived conditions for flatbands using local symmetries.

Applied conditions to Hamiltonians with long-range hoppings.

Extended framework to higher-dimensional Hamiltonians.

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.