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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Disordered Systems

Background:

  • Long-range hoppings in quantum systems lead to quantum multifractality, extending beyond typical Anderson transition properties.
  • Critical dynamics in these systems can display anomalous behaviors not seen in finite-dimensional Anderson transitions.

Purpose of the Study:

  • To propose a phenomenological model for wave packet expansion in long-range hopping systems.
  • To investigate multifractal properties and algebraic fat tails induced by long-range hoppings.
  • To analytically derive dynamics of moments and inverse participation ratios, linking them to multifractal dimensions.

Main Methods:

  • Development of a phenomenological model for wave packet expansion.
  • Analytical derivation of scaling laws for wave packet dynamics.
  • Numerical simulations using a Floquet model analogous to the power law random banded matrix ensemble.

Main Results:

  • The study analytically derives dynamics of moments and inverse participation ratios.
  • Numerical simulations validate predictions, showing dynamics deviate from single-parameter scaling laws.
  • Crucial finite-size and time-dependent scaling laws are established for these systems.

Conclusions:

  • Systems with long-range hoppings require novel scaling laws dependent on both size and time.
  • Findings are relevant for understanding many-body localization and Anderson localization on complex networks.
  • The inherent topology of the Hilbert space plays a key role in long-range effects.