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Critical dynamics of long-range quantum disordered systems.
Weitao Chen1,2,3, Gabriel Lemarié2,3,4, Jiangbin Gong1,2,3
1Department of Physics, National University of Singapore, Singapore.
Quantum disordered systems with long-range hoppings exhibit quantum multifractality and anomalous dynamics. New scaling laws involving both finite size and time are crucial for describing these systems, unlike standard Anderson transitions.
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.
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