On Transmission Node Structure in Interacting Systems

TL;DR

This paper investigates the structure of nodes in the retarded Green's function of interacting systems, revealing how interactions affect degeneracies, and characterizes these nodes in extended Hubbard models with implications for molecular spectra.

Contribution

It provides a general analysis of node behavior in interacting systems and introduces a polynomial-based characterization of node structures in extended Hubbard models.

Findings

Interactions split or lift degenerate nodes.

Degenerate nodes occur at boundaries between splitting and lifting regimes.

High degeneracies tend to be lifted rather than split.

Abstract

We provide a series of generic results regarding the structure of nodes in the retarded Green's function G of an interacting system, as exemplified by the extended Hubbard model. In particular: (1) due to an incompatibility between interactions of nearly any form and a precise definition of series propagation, degenerate geometric nodes are split or lifted by interactions; (2) degenerate nodes generically exist at the boundary between regimes of node splitting and node lifting and, in the presence of interactions, they require fine-tuning; (3) degenerate nodes are highly sensitive to perturbation and their sensitivity increases with their degeneracy. Moreover, for high degeneracies there is a tendency toward lifting rather than splitting. We also propose a characterization of the node structure in extended Hubbard models at arbitrary filling in terms of either the eigenvalues of G, or equivalently, the roots of a polynomial. This shows that "Mott nodes" previously predicted to occur in the transmission spectra of molecular radicals are fundamentally associated with nodes in the eigenvalues of the retarded Green's function that occur in open-shelled systems. This is accompanied by a low-energy two-pole approximation wherein each of the eigenvalues of G are mapped onto a Fermi-liquid-like renormalization of the Anderson model, for which the exact self-energy is provided.