Partial bosonisation for the two-dimensional Hubbard model: How well does it work?

TL;DR

This paper evaluates the effectiveness of partial bosonisation in the 2D Hubbard model, showing it accurately captures antiferromagnetic interactions and could enhance studies of competing orders.

Contribution

It demonstrates that partial bosonisation effectively describes electron interactions near antiferromagnetic order in the 2D Hubbard model, improving the functional renormalisation flow approach.

Findings

Interaction well described by bosonic exchange near antiferromagnetic order

Residual four-fermion vertex after subtraction is small

Partial bosonisation can improve accuracy in competing order studies

Abstract

Partial bosonisation of the two-dimensional Hubbard model focuses the functional renormalisation flow on channels in which interactions become strong and local order sets in. We compare the momentum structure of the four-fermion vertex, obtained on the basis of a patching approximation, to an effective bosonic description. For parameters in the antiferromagnetic phase near the onset of local antiferromagnetic order, the interaction of the electrons is indeed well described by the exchange of collective bosonic degrees of freedom. The residual four-fermion vertex after the subtraction of the bosonic exchange contribution is small. We propose that similar partial bosonisation techniques can improve the accuracy of renormalisation flow studies also for the case of competing order.