Nonlinear caging in All-Bands-Flat Lattices
Abstract
We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure of these lattices contains flat bands only, and cages non-interacting particles into compact localized eigenstates. We demonstrate that there always exist local unitary transformations that detangle such lattices into decoupled sites in dimension one. Starting from a detangled representation, inverting the detangling into entangling unitary transformations and extending to higher lattice dimensions, we arrive at an All-Bands-Flat generator for single particle states in any lattice dimension. The entangling unitary transformations are parametrized by sets of angles. For a given member of the set of all-bands-flat, additional short-range nonlinear interactions destroy caging in general, and induce transport. However, fine-tuned subsets of the unitary transformations allow to completely restore caging. We derive the necessary and sufficient fine-tuning conditions for nonlinear caging, and provide computational evidence of our conclusions for one-dimensional systems.
Cite
@article{arxiv.2004.11871,
title = {Nonlinear caging in All-Bands-Flat Lattices},
author = {Carlo Danieli and Alexei Andreanov and Thudiyangal Mithun and Sergej Flach},
journal= {arXiv preprint arXiv:2004.11871},
year = {2021}
}