SciPost Physics

SciPost Phys. 13, 046 (2022) · published 1 September 2022

• doi: 10.21468/SciPostPhys.13.3.046
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Abstract

We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-Andr\'e model. These spectral and eigenstate dualities are locally defined near the transition and can, in many cases, be explicitly constructed by considering relatively small commensurate approximants. The construction relies on auxiliary 2D Fermi surfaces obtained as functions of the phase-twisting boundary conditions and of the phase-shifting real-space structure. We show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to obtain mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously studied systems, including generalized Aubry-Andr\'e models and coupled Moir\'e chains. Our findings bring a new perspective to examine quasiperiodicity-induced extended-to-localized transitions in 1D, provide a working criterion for the appearance of mobility edges, and an explicit way to understand the properties of eigenstates close to and at the transition.

• Gonçalves et al., Renormalization group theory of one-dimensional quasiperiodic lattice models with commensurate approximants
  Phys. Rev. B 108, L100201 (2023) [Crossref]
• Wang et al., Observation of non-Abelian Anderson localization and transition in topolectrical circuits
  Phys. Rev. B 108, 144203 (2023) [Crossref]
• Gonçalves et al., Short-range interactions are irrelevant at the quasiperiodicity-driven Luttinger liquid to Anderson glass transition
  Phys. Rev. B 109, 014211 (2024) [Crossref]
• Borgnia et al., Localization as a consequence of quasiperiodic bulk-bulk correspondence
  Phys. Rev. B 107, 085111 (2023) [Crossref]
• Qi et al., Multiple localization transitions and novel quantum phases induced by a staggered on-site potential
  Phys. Rev. B 107, 224201 (2023) [Crossref]
• Zhou et al., Exact New Mobility Edges between Critical and Localized States
  Phys. Rev. Lett. 131, 176401 (2023) [Crossref]
• Duncan, Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals
  Phys. Rev. B 109, 014210 (2024) [Crossref]
• Roy et al., Critical and topological phases of dimerized Kitaev chain in presence of quasiperiodic potential
  Phys. Rev. B 107, 014202 (2023) [Crossref]
• Chen et al., Multifractality and prethermalization in the quasiperiodically kicked Aubry-André-Harper model
  Phys. Rev. B 109, 054202 (2024) [Crossref]
• Gonçalves et al., Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models
  Phys. Rev. Lett. 131, 186303 (2023) [Crossref]
• Wang et al., Engineering mobility in quasiperiodic lattices with exact mobility edges
  Phys. Rev. B 108, 174202 (2023) [Crossref]
• Madeira et al., Quasidisorder-induced topology
  Phys. Rev. B 106, 224505 (2022) [Crossref]
• Vu et al., Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
  Phys. Rev. B 107, 224206 (2023) [Crossref]
• Gonçalves et al., Quasiperiodicity hinders ergodic Floquet eigenstates
  Phys. Rev. B 108, 104201 (2023) [Crossref]