4.6 Article

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

Journal

PHYSICAL REVIEW B
Volume 106, Issue 20, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.106.205119

Keywords

-

Funding

  1. Council of Scientific and Industrial Research (CSIR) , India
  2. SERB [DST/INSPIRE/04/2014/002461]
  3. DST via the DST-INSPIRE Faculty Award [ERC-2018-SyG HERO-810451]
  4. European Research Council under the European Union
  5. Christ College Irinjalakuda
  6. [CRG/2019/003447]

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In this study, we investigate the effect of quasiperiodic Aubry-Andre disorder on the energy spectrum and eigenstates of a one-dimensional all-band-flat diamond chain. We find that the symmetric perturbation preserves compact localization while lifting the degeneracy, while the antisymmetric perturbation not only lifts the degeneracy but also destroys compact localization. Interestingly, all eigenstates exhibit multifractal behavior below a critical potential strength, while a central band of eigenstates continues to display extended behavior for arbitrarily large strengths of the potential.
We study the effect of quasiperiodic Aubry-Andre disorder on the energy spectrum and eigenstates of a one-dimensional all-band-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 nonergodic behavior 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 pi /4 rotated square lattice with the nearest and selective next-nearest-neighbor 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.

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