Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach

TL;DR

This paper uses a parquet dual fermion approach to analyze the Hubbard model at weak coupling, revealing the importance of nonlocal vertex corrections in pseudogap formation and explaining the nodal/antinodal dichotomy through fluctuation diagnostics.

Contribution

It introduces a boson exchange parquet solver for dual fermions that accurately captures nonlocal vertex effects and provides an unbiased fluctuation diagnostic of the self-energy.

Findings

Nonlocal vertex corrections enhance spin fluctuation coupling.

Pseudogap opens at higher temperature with parquet corrections.

Nodal and antinodal fermions are equally affected by spin fluctuations, but couple differently to incommensurate fluctuations.

Abstract

We apply the boson exchange parquet solver for dual fermions to the half-filled Hubbard model on a square lattice at small interaction. Our results establish that, in this regime, nonlocal vertex corrections play an important role in the formation of the pseudogap. Namely, in comparison to the simpler ladder approximation, these additional vertex corrections included in the parquet equations enhance the coupling of spin fluctuations with the quasiparticles. The pseudogap thus opens already at a higher temperature, in quantitative agreement with the numerically exact diagrammatic Monte Carlo. The representation of the parquet diagrams in terms of boson exchange facilitates large lattice sizes and gives rise to an unbiased fluctuation diagnostic of the self-energy, which does not rely on the Fierz ambiguity. The fluctuation diagnostic implies that nodal and antinodal fermions are affected equally by spin fluctuations with the exact commensurate nesting vector $(\pi,\pi)$. However, the antinode couples more efficiently to incommensurate fluctuations than the node, leading to the nodal/antinodal dichotomy. We corroborate this finding in terms of a spin-fermion-like calculation.