Subleading logarithmic behavior in the parquet formalism

TL;DR

This paper extends the parquet formalism to include both leading and next-to-leading logarithmic terms in the Fermi-edge singularity, providing a more comprehensive understanding of its logarithmic behavior.

Contribution

It formulates self-consistent equations that incorporate all leading and next-to-leading logarithmic terms, advancing the parquet solution beyond first order.

Findings

Numerical results in Matsubara formalism reveal characteristic power laws.

Multi-boson exchange diagrams are essential at the leading logarithmic level.

The approach offers new insights into the logarithmic behavior in parquet formalism.

Abstract

The Fermi-edge singularity in x-ray absorption spectra of metals is a paradigmatic case of a logarithmically divergent perturbation series. Prior work has thoroughly analyzed the leading logarithmic terms. Here, we investigate the perturbation theory beyond leading logarithms and formulate self-consistent equations to incorporate all leading and next-to-leading logarithmic terms. This parquet solution of the Fermi-edge singularity goes beyond the previous first-order parquet solution and sheds new light on the parquet formalism regarding logarithmic behavior. We present numerical results in the Matsubara formalism and discuss the characteristic power laws. We also show that, within the single-boson exchange framework, multi-boson exchange diagrams are needed already at the leading logarithmic level.