Finite-Energy Pseudoparticle Theory for the 1D Hubbard Model II: Holon and Spinon Dominant Processes for the Few-Electron Spectral Weight Properties

TL;DR

This paper develops a framework for analyzing finite-energy spectral functions in the 1D Hubbard model, identifying dominant holon and spinon processes that account for over 99% of spectral weight, and generalizes Hubbard band concepts.

Contribution

It introduces a method to evaluate few-electron spectral functions using holon and spinon processes, extending Hubbard band concepts across all interaction strengths.

Findings

Dominant holon and spinon processes account for over 99% of spectral weight.

Exact selection rules govern holon and spinon creation and annihilation.

Generalization of Hubbard bands to all Coulomb interaction values.

Abstract

In the first paper of this series it was found that the $\eta$-spin 1/2 holons, spin 1/2 spinons, and $c$ pseudoparticles whose occupancy configurations describe the energy eigenstates of the one-dimensional Hubbard model emerge from the electron - rotated-electron unitary transformation. In this second paper we discuss and clarify how the relation of the electrons to the above objects can be used in a program for evaluation of finite-energy few-electron spectral functions. As a first step, here we characterize the dominant holon and spinon microscopic physical processes that originate more than 99% of the few-electron spectral weight. These dominant processes are related to exact selection rules for the values of the number of holons and spinons generated or annihilated by application onto a ground state of rotated-electron operators. We also generalize the concepts of a lower Hubbard band and upper Hubbard bands to all values of on-site Coulombian repulsion.