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Anderson Localization Transition in Disordered Hyperbolic Lattices.

Anffany Chen1, Joseph Maciejko1, Igor Boettcher1

  • 1Theoretical Physics Institute, <a href="https://ror.org/0160cpw27">University of Alberta</a>, Edmonton, Alberta T6G 2E1, Canada and Department of Physics, <a href="https://ror.org/0160cpw27">University of Alberta</a>, Edmonton, Alberta T6G 2E1, Canada.

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Summary
This summary is machine-generated.

We investigated Anderson localization in disordered systems on hyperbolic lattices. Our findings reveal a distinct localization transition with large critical disorder strengths and significant finite-size effects.

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Area of Science:

  • Condensed matter physics
  • Disordered systems
  • Geometric lattices

Background:

  • Anderson localization describes wave function confinement in disordered systems.
  • Hyperbolic lattices offer unique geometries between 2D crystalline and Bethe lattices.
  • Understanding localization on these intermediate geometries is crucial.

Purpose of the Study:

  • To investigate Anderson localization in disordered tight-binding models on hyperbolic lattices.
  • To determine the critical disorder strengths and exponents for localization.
  • To analyze finite-size effects on hyperbolic lattices.

Main Methods:

  • Utilized computational group theory to construct large hyperbolic lattice systems.
  • Employed periodic boundary conditions to approximate the thermodynamic limit.
  • Performed numerical simulations to study Anderson localization transitions.

Main Results:

  • Demonstrated the existence of an Anderson localization transition on {8,3} and {8,8} hyperbolic lattices.
  • Observed unusually large critical disorder strengths.
  • Identified a strong finite-size effect in the level statistics.

Conclusions:

  • Hyperbolic lattices exhibit Anderson localization transitions.
  • The critical disorder strengths are significantly larger than in some other lattice types.
  • Finite-size effects play a crucial role in understanding localization phenomena on these lattices.