Disorder perturbed Flat Bands II: a search for criticality
arXiv:1807.02436 · doi:10.1103/PhysRevB.98.184202
Abstract
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing disorder, insensitive to disorder strength, in weak disorder limit; the spectral statistics at the critical point corresponds to a critical Brownian ensemble, a non-equilibrium universality class of random matrix ensembles, intermediate to Poisson and Gaussian orthogonal ensemble. With increasing disorder, the statistics again approaches Poisson limit indicating a localization -> extended -> localization transition of the wave-dynamics. Our analysis also reveals a hidden connection of weakly disordered flat bands to a wide-range of other complex systems including standard Anderson Hamiltonian.
29 Pages, 6 Figures. First version of arXiv:1712.03523 divided into two parts, more details and new references included, no change in results
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Cited by in corpus (15)
- Flat-band many-body localization and ergodicity breaking in the Creutz ladder
- Flat-band engineering in tight-binding models: Beyond the nearest-neighbor hopping
- Extended flat-bands, entanglement and topological properties in a Creutz ladder
- Localization and criticality in antiblockaded 2D Rydberg atom arrays
- Disorder effects in the two-dimensional Lieb lattice and its extensions
- Interplay and competition between disorder and flat band in an interacting Creutz ladder
- Localization, phases and transitions in the three-dimensional extended Lieb lattices
- Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
- Spectral statistics of multi-parametric Gaussian ensembles with chiral symmetry
- Molecular-orbital representation with random U(1) variables
- Interplay of many-body interactions and quasiperiodic disorder in the all-band-flat diamond chain
- Scaling laws for weakly disordered 1D flat bands
- Transition to chaos in extended systems and their quantum impurity models
- Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness
- Many body density of states in the edge of the spectrum: non-interacting limit