Four-point vertex in the Hubbard model and partial bosonization

TL;DR

This paper investigates magnetic and superconducting instabilities in the 2D t-t'-Hubbard model using a functional renormalization group approach, employing partial bosonization to analyze the four-point vertex and compute pseudocritical temperatures.

Contribution

It introduces an efficient parametrization of the four-point vertex via partial bosonization within the FRG framework for the Hubbard model.

Findings

Effective couplings increase with length scale.

Pseudocritical temperatures for local order are computed.

Exchange of composite bosons explains instability growth.

Abstract

Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial bosonization. The exchange of composite bosons in the magnetic, charge density and superconducting channels accounts for the increase of the effective couplings with increasing length scale. We compute the pseudocritical temperature for the onset of local order in various channels.