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Duality in Power-Law Localization in Disordered One-Dimensional Systems.

X Deng1, V E Kravtsov2,3, G V Shlyapnikov4,5,6,7,8

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In one-dimensional systems, excitations in pinned particles exhibit power-law localization for any hopping exponent. This study reveals a new universality class with duality between long-range and short-range hops.

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Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Quantum Mechanics

Background:

  • Many physical systems exhibit excitation transport between pinned particles.
  • This transport can be modeled using single-particle models with power-law hopping (1/r^a).
  • Randomly spaced particles introduce peculiar disorder, influencing localization properties.

Purpose of the Study:

  • To investigate the localization properties of eigenstates in one-dimensional systems with power-law hopping.
  • To identify if a new universality class emerges from these models.
  • To explore the duality between long-range and short-range hopping regimes.

Main Methods:

  • Analysis of single-particle models with power-law hopping (1/r^a).
  • Examination of one-dimensional systems with randomly spaced pinned particles.
  • Characterization of eigenstate localization properties.

Main Results:

  • Almost all eigenstates in one-dimensional systems are power-law localized for any a>0.
  • A new universality class of power-law hopping models is identified.
  • A duality exists between long-range (a<1) and short-range (a>1) hopping systems.

Conclusions:

  • Power-law localization is a robust feature in these disordered one-dimensional systems.
  • The identified universality class offers a new framework for understanding disordered quantum systems.
  • The duality suggests universal scaling behavior regardless of hop range.