Mott transitions in the periodic Anderson model

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.
• 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.