Electrons, pseudoparticles, and quasiparticles in one-dimensional interacting electronic systems

TL;DR

This paper explores the relationship between electrons, pseudoparticles, and quasiparticles in one-dimensional Hubbard chains, providing explicit calculations and discussing implications for higher-dimensional systems and potential instabilities.

Contribution

It introduces a singular transformation between electron and pseudoparticle operators and generalizes quasiparticles to many-pseudoparticle objects in 1D systems.

Findings

Explicit electron renormalization factor at Fermi points

Calculated self-energy and vertex functions

Discussed potential instabilities like Cooper pair formation

Abstract

We find the singular transformation between the electron operator and the pseudoparticle operators for the Hubbard chain. We generalize the concept of quasiparticle to one-dimensional electronic systems which in 1D refers to many-pseudoparticle objects. We obtain explicit results for the electron renormalization factor, self energy, and vertex functions at the Fermi points. We also discuss the possible connection of our results to higher dimensions and explore the possibilities of instabilities in the interacting problem such as the formation of Cooper pairs.