Electrons, pseudoparticles, and quasiparticles in the one-dimensional many-electron problem

TL;DR

This paper extends the concept of quasiparticles in one-dimensional interacting electron systems, introducing complex excitations that combine charge and spin pseudoparticles, and explores their implications for Fermi-liquid behavior across dimensions.

Contribution

It generalizes quasiparticle concepts for 1D systems, showing their composite nature and the singular electron-quasiparticle transformation, with implications for higher-dimensional quantum liquids.

Findings

Quasiparticles in 1D are composite of pseudoparticles and topological moments.

Electron-quasiparticle overlap is absent in 1D, indicating a singular transformation.

Existence of Fermi-surface quasiparticles in 1D and 3D suggests possible similar behavior in intermediate dimensions.

Abstract

We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The $\uparrow $ and $\downarrow $ quasiparticles recombine the pseudoparticle colors $c$ and $s$ (charge and spin at zero magnetic field) and are constituted by one many-pseudoparticle {\it topological momenton} and one or two pseudoparticles. These excitations cannot be separated. We consider the case of the Hubbard chain. We show that the low-energy electron -- quasiparticle transformation has a singular charater which justifies the perturbative and non-perturbative nature of the quantum problem in the pseudoparticle and electronic basis, respectively. This follows from the absence of zero-energy electron -- quasiparticle overlap in 1D. The existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D) many-electron systems suggests there existence in quantum liquids in dimensions 1$<$D$<$3. However, whether the electron -- quasiparticle overlap can vanish in D$>$1 or whether it becomes finite as soon as we leave 1D remains an unsolved question.