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Related Experiment Video

Updated: Mar 15, 2026

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing
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Mott transitions in the periodic Anderson model.

David E Logan, Martin R Galpin, Jonathan Mannouch

    Journal of Physics. Condensed Matter : an Institute of Physics Journal
    |September 13, 2016
    PubMed
    Summary

    This study explores the periodic Anderson model (PAM) and its Mott transitions using dynamical mean-field theory. It reveals a new low-energy model for Mott insulators and provides exact results for their properties.

    Area of Science:

    • Condensed Matter Physics
    • Quantum Many-Body Theory

    Background:

    • The periodic Anderson model (PAM) is a key model for understanding strongly correlated electron systems.
    • Mott transitions, driven by electron-electron interactions, lead to insulating states crucial in materials science.

    Purpose of the Study:

    • To investigate interaction-driven Mott transitions within the PAM.
    • To characterize Mott insulators of both Mott-Hubbard and charge-transfer types.
    • To derive an effective low-energy model describing the PAM near a Mott transition.

    Main Methods:

    • Dynamical Mean-Field Theory (DMFT) for analyzing the PAM.
    • Exact results to deduce the PAM phase diagram across all parameters.
    • Numerical Renormalization Group (NRG) calculations to confirm and supplement findings.

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  • A two-self-energy description for locally degenerate, non-Fermi liquid Mott insulators.

    • Main Results:

    • The PAM phase diagram includes metallic, Mott, Kondo, and band insulator phases.
    • An effective one-band Hubbard model describes the PAM near a Mott transition, with exponentially decaying, non-nearest-neighbor hoppings.
    • Exact results are obtained for local moment, charge, and renormalized levels in Mott insulators.
    • A generalization of Luttinger's theorem to Mott insulators is presented.

    Conclusions:

    • The study provides a comprehensive understanding of Mott transitions and insulators in the PAM.
    • The derived effective model and exact results offer new insights into strongly correlated electron systems.
    • The work establishes a framework for describing complex insulating states in condensed matter.