Extended Falicov-Kimball model: Hartree-Fock vs DMFT approach

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• The extended Falicov-Kimball model is a key model for understanding electron correlations in materials.
• Investigating phase transitions and metal-insulator transitions is crucial for materials science.
• Comparing approximate methods like Hartree-Fock approach (HFA) with rigorous methods like dynamical mean-field theory (DMFT) is essential for validating theoretical frameworks.

Purpose of the Study:

• To compare the extended Falicov-Kimball model's properties calculated via Hartree-Fock approach (HFA) with rigorous dynamical mean-field theory (DMFT) results.
• To assess the validity and limitations of HFA in describing ground-state and finite-temperature properties of the model.
• To identify specific phase transitions and electronic behaviors that HFA can and cannot accurately capture.

Main Methods:

• Application of the Hartree-Fock approach (HFA) to the extended Falicov-Kimball model at half-filling across various crystal lattices.
• Rigorous derivation of results using the dynamical mean-field theory (DMFT) for comparison.
• Analysis of ground-state properties and transitions at both zero and small temperatures.

Main Results:

• HFA accurately reproduces ground-state properties and is equivalent to the exact DMFT solution for the extended Falicov-Kimball model.
• HFA qualitatively captures transitions between ordered phases at U = 2V and continuous order-disorder transitions at small temperatures.
• HFA fails to describe the merging of discontinuous and continuous transition boundaries, the isolated-critical point, and certain metal-insulator transitions observed in DMFT.

Conclusions:

• HFA provides a valuable and often accurate approximation for the extended Falicov-Kimball model, particularly for ground-state properties.
• The limitations of HFA become apparent in describing complex phase boundary behaviors and specific electronic transitions like metal-insulator transitions.
• DMFT remains essential for a complete and rigorous understanding of the model's rich phase diagram and diverse electronic behaviors.