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

Kilian Fraboulet1, Sarah Heinzelmann1, Pietro M Bonetti2

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The new single-boson exchange (SBE) formulation for functional renormalization group (fRG) calculations offers significant algorithmic advantages for the two-dimensional Hubbard model. This method reduces computational effort and improves stability at phase transitions, unlike conventional fRG approaches.

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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.