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Universal relation between spectral and wavefunction properties at criticality.

Simon Jiricek1,2, Miroslav Hopjan2,3, Vladimir Kravtsov4

  • 1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia.

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PubMed
Summary
This summary is machine-generated.

We discovered a universal relationship between spectral compressibility and wavefunction fractal dimension in quantum critical systems. This finding suggests a new universality class for critical phenomena in disordered quantum systems.

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critical behaviorspectral statisticswavefunction multifractality

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Area of Science:

  • Condensed Matter Physics
  • Quantum Chaos
  • Disordered Systems

Background:

  • Quantum chaotic systems display universal properties like level repulsion and delocalized wavefunctions.
  • Localized wavefunctions lead to Poisson statistics and no level repulsion.
  • Critical systems at the boundary between chaos and localization exhibit unique behavior.

Purpose of the Study:

  • Investigate universality at the quantum chaos-localization critical point.
  • Explore the relationship between spectral compressibility (χ) and wavefunction fractal dimension (dF).
  • Test this relationship in various physical systems with different symmetries and hopping types.

Main Methods:

  • Numerical analysis of Anderson models (3-5 dimensions) and random banded matrices.
  • Studying systems with both local and nonlocal hopping, with and without time-reversal symmetry.
  • Testing a closed-form expression for spectral compressibility in random banded matrices.

Main Results:

  • Confirmed a simple, universal relation between spectral compressibility and wavefunction fractal dimension across investigated systems.
  • Validated the accuracy of a derived closed-form expression for spectral compressibility.
  • Derived a universal function relating spectral compressibility to the averaged level spacing ratio (r).

Conclusions:

  • The relation [Formula: see text] appears to be a universal property for a wide range of critical models.
  • The findings suggest a new universality class at the quantum critical point.
  • A universal function [Formula: see text] is established for critical systems based on spectral properties.