Conservation, crossing symmetry, and completeness in diagrammatic theories

2024/01/03 by Frederick Green, Green, Frederick
Physics and Astronomy · Chemistry · #Advanced Chemical Physics Studies #Spectroscopy and Quantum Chemical Studies #Advanced NMR Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2401.01682

Abstract

The diagrammatic analysis of interacting particle assemblies harbors a fundamental mismatch between two of its main implementations: Phi-derivable (conserving) approximations and parquet (crossing symmetric) models. No termwise expansion, short of the exact theory itself, can be both conserving and crossing symmetric. This work applies the Kraichnan embedded-Hamiltonian formalism for strongly coupled systems to investigate consistency of the interplay between purely pair-mediated correlations and pair-irreducible ones. The approach sheds a different light on the issue of crossing symmetry versus conservation. In the process, the parquet equations acquire a different formulation.

Related

• Diagrammatic bosonisation, aspects of criticality, and the Hohenberg-Mermin-Wagner Theorem in parquet approaches
• Generating functional for the full parquet approximation
• Embedded Representations and Quasi-Dynamical Symmetry
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• The families of Hamiltonians sharing common symmetry structure