From infinite to two dimensions through the functional renormalization group.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Computational Physics

Background:

• Strongly correlated fermions present significant challenges in condensed matter physics.
• Accurate theoretical treatments are crucial for understanding complex electronic behaviors.
• Existing methods often struggle to capture both local and nonlocal correlation effects simultaneously.

Purpose of the Study:

• To develop a novel, unbiased, and nonperturbative theoretical framework for strongly correlated fermions.
• To combine the strengths of dynamical mean-field theory (DMFT) and functional renormalization group (fRG).
• To enable systematic inclusion of nonlocal correlations beyond local approximations.

Main Methods:

• The proposed method integrates DMFT for local correlations with fRG for nonlocal correlations.
• DMFT provides a nonperturbative treatment of local electronic interactions.
• fRG extends the treatment to include nonlocal correlations through its flow equations.

Main Results:

• The combined DMFT-fRG approach offers a systematic way to include nonlocal correlations.
• Numerical simulations were performed for the two-dimensional Hubbard model at half filling.
• The feasibility of the novel scheme was demonstrated through these calculations.

Conclusions:

• The integrated DMFT-fRG method provides a powerful new tool for studying strongly correlated systems.
• This approach allows for a more complete and accurate description of electronic correlations.
• The method holds promise for advancing our understanding of various condensed matter phenomena.