Flat-band-based multifractality in the all-band-flat diamond chain

Abstract

We study the effect of quasiperiodic Aubry-André disorder on the energy spectrum and eigenstates of a one-dimensional all-bands-flat (ABF) diamond chain. The ABF diamond chain possesses three dispersionless flat bands with all the eigenstates compactly localized on two unit cells in the zero disorder limit. The fate of the compact localized states in the presence of the disorder depends on the symmetry of the applied potential. We consider two cases here: a symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. Remarkably, the symmetrically perturbed lattice preserves compact localization, although the degeneracy is lifted. When the lattice is perturbed antisymmetrically, not only is the degeneracy is lifted but compact localization is also destroyed. Fascinatingly, all eigenstates exhibit a multifractal nature below a critical strength of the applied potential. A central band of eigenstates continue to display an extended yet non-ergodic behaviour for arbitrarily large strengths of the potential. All other eigenstates exhibit the familiar Anderson localization above the critical potential strength. We show how the antisymmetric disordered model can be mapped to a $\frac{\pi }{4}$ rotated square lattice with nearest and selective next-nearest neighbour hopping and a staggered magnetic field - such models have been shown to exhibit multifractality. Surprisingly, the antisymmetric disorder (with an even number of unit cells) preserves chiral symmetry - we show this by explicitly writing down the chiral operator.

18 pages, 11 figures

References in corpus (25)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Observation of a localized flat-band state in a photonic Lieb lattice
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Flat Bands Under Correlated Perturbations
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Anderson localisation in tight-binding models with flat bands
• Chiral Flat Bands: Existence, Engineering and Stability
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Flat bands with higher Chern number in pyrochlore slabs
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Bose-Einstein Condensates in Spin-Orbit Coupled Optical Lattices: Flat Bands and Superfluidity
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Entanglement entropy and multifractality at localization transitions
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Topological flat Wannier-Stark bands
• Anderson transition in systems with chiral symmetry
• Symmetry-protected localized states at defects in non-Hermitian systems
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Multifractality in aperiodic quantum spin chains

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