4.6 Article

Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-Andre-Harper modulation

期刊

PHYSICAL REVIEW B
卷 106, 期 2, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.106.024204

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资金

  1. ERC AdG NOQIA
  2. Ministerio de Ciencia y Innovation Agencia Estatal de Investigaciones [PGC2018-097027-BI00, CEX2019-000910-S, FIDEUA PID2019-106901GB-I00, QUANTERA MAQS PCI2019-111828-2, QUANTERA DYNAMITE PCI2022-132919, QUSPIN RTC2019-007196-7]
  3. European Union NextGenerationEU [PRTR C17.I1]
  4. Fundacio Cellex
  5. Fundacio Mir-Puig
  6. Generalitat de Catalunya (CERCA program (AGAUR)) [2017 SGR 134, U16-011424]
  7. ERDF Operational Program of Catalonia 2014-2020
  8. Barcelona Supercomputing Center MareNostrum [FI-2022-1-0042]
  9. EU Horizon 2020 FET-OPEN OPTOlogic [899794]
  10. National Science Centre, Poland [2016/20/W/ST4/00314]
  11. European Union [101029393, 847648, 100010434 LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013]
  12. la Caixa Foundation [LCF/BQ/PR20/11770012, 100010434]
  13. Barcelona Supercomputing Center [FI-2022-1-0042]
  14. Generalitat de Catalunya (European Social Fund FEDER)

向作者/读者索取更多资源

In this study, we generalize the phase diagram of the Kitaev chain model in the presence of quasiperiodic potentials by investigating the localization properties of the Aubry-Andre-Harper model with long-range hopping and superconducting pairing amplitudes. We find transitions between ergodic, localized, and multifractal states, as well as energy-dependent transitions from ergodic to multifractal states for certain parameters. The size of the intermediate multifractal region depends on the superconducting pairing term and energy band, and the transitions are characterized by hybridization of bands with different localization properties.
In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized, and multifractal states. In this work, we generalize these results by studying the localization properties of the Aubry-Andre-Harper model in the presence of long-range hopping and superconducting pairing amplitudes. These amplitudes decay with power-law exponents xi and alpha, respectively. To this end, we review and compare a toolbox of global and local characterization methods in order to investigate different types of transitions between ergodic, localized, and multifractal states. We report energy-dependent transitions from ergodic to multifractal states for pairing terms with alpha < 1 and energy-dependent transitions from ergodic to localized states with an intermediate multifractal region for alpha > 1. The size of the intermediate multifractal region depends not only on the value of the superconducting pairing term Delta, but also on the energy band. The transitions are not described by a mobility edge, but instead we report hybridization of bands with different types of localization properties. This leads to coexisting multifractal regimes where fractal dimensions follow different distributions.

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