Related papers: Single and double linear and nonlinear flatband ch…

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 nonlinear caging, i.e. keeps compact excitations…

A spinless two-band model is studied in infinite dimension limit. Starting from the atomic limit, the formal exact solution of the model is obtained by means a perturbative treatment of the hopping and hybridisation terms. The model is…

This work explores a holographic proposal to describe light nuclide spectroscopy by considering extensions to the well-known bottom-up AdS/QCD proposals, the hardwall and softwall models. We also propose an alternative description inspired…

We introduce and explore patterned lattices consisting of coupled isospectral cells that vary across the lattice. The isospectrality of the cells is encapsulated in the phase that characterizes each cell and can be designed at will such…

We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of…

We analyze the localization properties of two dimensional systems based on partite lattices with a basis. Contrary to standard results, we find that a band of critical states emerges for systems in the unitary class A preserving spin…

A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a…

We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized…

A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…

We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete…

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically…

The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schr\"{o}dinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is…

We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different…

Interactions between stacked two-dimensional (2D) atomic crystals can radically change their properties, leading to essentially new materials in terms of the electronic structure. Here we show that monolayers placed on an atomically flat…

We predict multiband vector Plasmonic Lattice Solitons (PLSs) in metal-dielectric waveguide arrays, in both focusing and defocusing nonlinearities. Such vector solitons consist of two components originating from different transmission…

Based on the mean-field method applied either to the extended single-band Hubbard model or to the single-band Peierls-Hubbard Hamiltonian we study the stability of both site-centered and bond-centered charge domain walls. The difference in…

We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasi-periodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. {\bf B 48}, 4192 (1993) ], within the framework…

We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…

Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures…

We study localization and flat-band formation in lattices generated by repeated edge inflation of square, honeycomb, and triangular parent lattices. Replacing each bond by a finite tight-binding chain produces several distinct classes of…