Parquet theory for correlated thermodynamic Greens functions

TL;DR

This paper develops a parquet theoretical framework for correlated thermodynamic Greens functions, extending diagrammatic techniques to include cumulant expansions and crossing-invariant equations for two-particle correlations.

Contribution

It introduces a self-consistent parquet formalism for two-body Greens functions derived from cumulant expansions, generalizing existing diagrammatic methods.

Findings

Reproduces conventional parquet diagrammatic techniques.

Derives crossing-invariant linearized parquet equations.

Provides a basis for analyzing correlated two-particle Greens functions.

Abstract

We address the problem of finding self-consistent parquet equations for two-body correlated Greens functions that arise out of a cumulant expansion. The general theory as developed for non-relativistic electron systems reproduces the conventional two-body parquet diagrammatic technique for the vertex functions. As an application, the crossing-invariant linearized basic parquet equations are treated for the correlated two-particle Greens function.