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Random matrices with correlated elements: a model for disorder with interactions.

Pragya Shukla1

  • 1Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 24, 2005
PubMed
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Disordered interacting systems exhibit correlated random states, behaving like multiparametric random matrices. Their eigenvalue correlations are described by Brownian ensembles, revealing critical behaviors and universal level correlations.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Disorder in quantum systems leads to complex state interactions and randomization.
  • The Hamiltonian of such systems can be modeled as a multiparametric random matrix with correlated elements.

Purpose of the Study:

  • To describe eigenvalue correlations in disordered interacting systems.
  • To utilize the analogy with random matrix theory to understand level statistics.

Main Methods:

  • Modeling the Hamiltonian as a multiparametric random matrix with correlated elements.
  • Applying single parametric Brownian ensembles to describe eigenvalue correlations.

Main Results:

  • Eigenvalue correlations are accurately described by single parametric Brownian ensembles.

Related Experiment Videos

  • The analogy reveals critical point behavior distinct from noninteracting systems.
  • Extended states are possible even in one-dimensional systems.

    • Conclusions:

    • Brownian ensembles provide a universal framework for understanding level correlations in disordered interacting systems.
    • This approach elucidates key features of level statistics, including critical phenomena and the existence of extended states.