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Nonlinear sigma model approach for level correlations in chiral disordered systems.

Kazutaka Takahashi1

  • 1Theoretische Physik III, Ruhr-Universität Bochum, 44780 Bochum, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
Summary

We analyzed disordered systems with chiral unitary symmetry (AIII symmetry) using a random matrix model. Our findings reveal unique renormalization of mean level spacing, differing from traditional systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Chaos
  • Disordered Systems

Background:

  • Understanding level correlations in disordered systems is crucial for quantum chaos.
  • Chiral unitary symmetry (AIII) presents unique challenges in theoretical analysis.
  • Previous studies utilized different models, necessitating comparison with novel approaches.

Purpose of the Study:

  • To investigate level correlations in disordered systems with AIII symmetry.
  • To derive and analyze a supersymmetric nonlinear sigma model.
  • To compare results with existing literature and traditional nonchiral systems.

Main Methods:

  • Employing a random matrix model with finite correlation length.
  • Deriving a supersymmetric nonlinear sigma model.

Related Experiment Videos

  • Calculating density of states and two-level correlation function using established methods (Sov. Phys. JETP 60, 656 (1994); Phys. Rev. Lett. 75, 902 (1995)).

    • Main Results:

    • The derived supersymmetric nonlinear sigma model provides a framework for studying AIII symmetry.
    • Density of states and two-level correlation function were calculated and expressed via spectral determinant.
    • A renormalization of mean level spacing was identified, a phenomenon absent in traditional systems.

    Conclusions:

    • The study successfully models disordered systems with AIII symmetry, offering new insights.
    • The spectral determinant provides a unified expression for results, analogous to nonchiral systems.
    • The renormalization of mean level spacing highlights a key distinction of these chiral systems.