Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak...

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Computational Physics

Background:

• The two-dimensional Hubbard model is a key model for understanding strongly correlated electron systems.
• Functional Renormalization Group (fRG) is a powerful non-perturbative method for studying quantum systems.
• The single-boson exchange (SBE) formulation offers a new algorithmic approach within fRG.

Purpose of the Study:

• To demonstrate the algorithmic benefits of the SBE formulation for one-loop fRG.
• To apply the SBE-fRG to the two-dimensional Hubbard model on a square lattice.
• To analyze fermion-boson Yukawa couplings and physical susceptibilities.

Main Methods:

• Application of the single-boson exchange (SBE) formulation of the one-loop functional renormalization group (fRG).
• Study of the two-dimensional Hubbard model on a square lattice.
• Analysis of fermion-boson Yukawa couplings and physical susceptibilities as a function of temperature and interaction strength.
• Comparison with the conventional fermionic fRG decomposition.

Main Results:

• The rest functions in the SBE algorithm have a negligible role in the weak-coupling regime above the pseudo-critical temperature.
• Unlike conventional fRG, SBE rest functions remain finite at the pseudo-critical transition.
• The SBE formulation significantly reduces numerical effort for the two-particle vertex function.

Conclusions:

• The SBE formulation of fRG provides algorithmic advantages for studying the two-dimensional Hubbard model.
• The SBE approach shows improved stability and reduced computational cost compared to conventional fRG.
• This work paves the way for future extensions of fRG to multiboson and multiloop calculations.