Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis

Cornelia Hille,Daniel Rohe,Sabine Andergassen,Carsten Honerkamp

doi:10.1103/physrevresearch.2.033068

Abstract

Using the recently introduced multiloop extension of the functional renormalization group, we compute the frequency- and momentum-dependent self-energy of the two-dimensional Hubbard model at half filling and weak coupling. We show that, in the truncated-unity approach for the vertex, it is essential to adopt the Schwinger-Dyson form of the self-energy flow equation in order to capture the pseudogap opening. We provide an analytic understanding of the key role played by the flow scheme in correctly accounting for the impact of the antiferromagnetic fluctuations. For the resulting pseudogap, we present a detailed numerical analysis of its evolution with temperature, interaction strength, and loop order.

Highlights

In correlated electrons physics, the term pseudogap is usually associated with a gaplike suppression of the low-energy spectral weight that occurs without a direct connection to a phase transition
We provide a reasoning for the lack of pseudogap physics in previous conventional one-loop (1 ) flows of the self-energy and demonstrate that its replacement by the derivative of the SDE yields the expected gap opening
II we introduce the Hubbard model and describe the SDE flow scheme employed for the computation of the self-energy, which in the truncated-unity fRG (TUfRG) framework correctly accounts for the form-factor projections in the different channels

Summary

INTRODUCTION

The term pseudogap is usually associated with a gaplike suppression of the low-energy spectral weight that occurs without a direct connection to a phase transition. In contrast to the pseudogap originating from strongcoupling effects, the weak-coupling mechanism is induced by long-range antiferromagnetic (AF) correlations [7,17,18,19,20,22,23,24,25] For this reason the half-filled Hubbard model without next-nearest-neighbor hopping has been considered, with the two-particle self-consistent approach [22], the dynamical cluster approximation [21], the dynamical vertex approximation [25], and recently with the parquet approximation.

The 2D Hubbard model

Functional renormalization group

Self-energy flow versus Schwinger-Dyson equation

Towards full multiloop fRG

Difference of self-energy flow schemes in the TUfRG

CONCLUSIONS AND OUTLOOK