# Nonlinear caging in all-bands-flat lattices

@article{Danieli2021NonlinearCI, title={Nonlinear caging in all-bands-flat lattices}, author={Carlo Danieli and Alexei Andreanov and Thudiyangal Mithun and Sergej Flach}, journal={Physical Review B}, year={2021} }

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… Expand

#### 8 Citations

Anti-PT Flatbands

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Arindam Mallick, ∗ Nana Chang, 2, 3, † Alexei Andreanov, 4, ‡ and Sergej Flach 4, § Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon, Korea, 34126 Beijing… Expand

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Nonlinear networks can host spatially compact time periodic solutions called compact breathers. Such solutions can exist accidentally (i.e. for specific nonlinear strength values) or parametrically… Expand

Flat bands by latent symmetry

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Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting… Expand

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Translationally invariant finetuned single-particle lattice Hamiltonians host flat bands only. Suitable short-range many-body interactions result in complete suppression of particle transport due to… Expand

Metal-insulator transition in infinitesimally weakly disordered flat bands

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- Physical Review B
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We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d+1) local unitary… Expand

One-dimensional
2n
-root topological insulators and superconductors

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Square-root topology is a recently emerged subfield describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite… Expand

Quantum caging in interacting many-body all-bands-flat lattices

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- Physical Review B
- 2021

We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [arXiv:2004.11871] we derived the subset of these networks which preserves… Expand

Wannier-Stark flatbands in Bravais lattices

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We systematically construct flatbands for tight-binding models on simple Bravais lattices in space dimension $d \geq 2$ in the presence of a static uniform DC field. Commensurate DC field directions… Expand

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