Parquet decomposition calculations of the electronic self-energy

TL;DR

This paper uses parquet decomposition within DMFT and DCA to analyze the electronic self-energy in the Hubbard model, revealing dominant spin processes and singularities linked to pseudogap formation.

Contribution

It introduces a detailed parquet decomposition approach to non-perturbative calculations, highlighting differences from fluctuation diagnostics and connecting singularities to pseudogap physics.

Findings

Self-energies in underdoped regime dominated by spin scattering

Singularities in parquet terms appear before Mott transition

Parquet singularities linked to pseudogap and RVB state formation

Abstract

The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.