Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling

TL;DR

This paper uses a functional renormalization group approach to study the frequency-dependent vertex functions of the (t,t')-Hubbard model at Van Hove filling, revealing the importance of frequency dependence in the effective interactions.

Contribution

It introduces a detailed frequency-dependent analysis of the vertex functions in the (t,t')-Hubbard model, including channel decomposition and self-energy effects, advancing previous frequency-independent studies.

Findings

Higher pseudo-critical scales found with frequency dependence.

Smaller region of d-wave superconductivity when including frequency effects.

Significant contribution from forward scattering with finite frequency exchange.

Abstract

We present a functional renormalization group calculation for the two-dimensional (t,t')-Hubbard model at Van Hove filling. Using a channel decomposition we describe the momentum and frequency dependence of the vertex function in the normal phase. Compared to previous studies that neglect frequency dependences we find higher pseudo-critical scales and a smaller region of d-wave superconductivity. A large contribution to the effective interaction is given by a forward scattering process with finite frequency exchange. We test different frequency parameterizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.