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

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References

SHOWING 1-10 OF 47 REFERENCES
Quantum caging in interacting many-body all-bands-flat lattices
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 preservesExpand
Colloquium : Many-body localization, thermalization, and entanglement
Thermalizing quantum systems are conventionallydescribed by statistical mechanics at equilib-rium. However, not all systems fall into this category, with many-body localization providinga genericExpand
Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models ofExpand
Nonlinear dynamics of Aharonov-Bohm cages
The interplay of $\pi$-flux and lattice geometry can yield full localization of quantum dynamics in lattice systems, a striking interference phenomenon known as Aharonov-Bohm caging. At the level ofExpand
Nonlinear symmetry breaking of Aharonov-Bohm cages
We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm cagingExpand
Quantum Network Transfer and Storage with Compact Localized States Induced by Local Symmetries.
TLDR
A method to equip any network featuring static perfect state transfer of single-site excitations with compact localized states, thus increasing the storage ability of these networks, and it is shown that these compact localization states can likewise be perfectly transferred through the corresponding network by suitable, time-dependent modifications. Expand
Universal d=1 flat band generator from compact localized states
The band structure of some translationally invariant lattice Hamiltonians contains strictly dispersionless flatbands(FB). These are induced by destructive interference, and typically host compactExpand
Wave Packet Spreading with Disordered Nonlinear Discrete-Time Quantum Walks.
TLDR
A novel unitary map toolbox-discrete-time quantum walks originally designed for quantum computing-is used to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium and observes that the universal subdiffusion persists over an additional four decades reaching "astronomic" times 2×10^{12}. Expand
Artificial flat band systems: from lattice models to experiments
Abstract Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation,Expand
Compact localized states and flat bands from local symmetry partitioning
We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation ofExpand
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