Finite-Energy Landau Liquid Theory for the 1D Hubbard Model: Pseudoparticle Energy Bands and Degree of Localization/Delocalization

TL;DR

This paper investigates the finite-energy spectral properties of the 1D Hubbard model, focusing on pseudoparticle energy bands and their relation to electron localization, providing insights into spectral weight distributions.

Contribution

It introduces a detailed analysis of pseudoparticle energy bands and their dependence on various parameters, advancing understanding of finite-energy spectral features in the 1D Hubbard model.

Findings

Double-occupancy spectra reveal localization/delocalization characteristics.

Pseudoparticle energy bands depend on momentum, interaction strength, and density.

Band shapes influence spectral weight distribution in energy-momentum space.

Abstract

This paper is part of a broader study whose main goal is the study of the finite-energy spectral properties of the non-perturbative one-dimensional (1D) Hubbard model and the evaluation of finite-energy correlation-function expressions. Here we study the deviations from the ground state values of double occupancy which result from creation or annihilation of holons, spinons, and pseudoparticles. The band-momentum dependence of the obtained double-occupancy spectra provides important information on the degree of localization/delocalization of the real-space lattice electron site distribution configurations associated with the pseudoparticles. We also study the band-momentum, on-site electronic repulsion, and electronic density dependence of the pseudoparticle energy bands. The shape of these bands plays an important role in the finite-energy spectral properties of the model. Such a shape defines the form of the lines in the momentum-energy/frequency plane where the peaks and edges of the one-electron and two-electron spectral weight of physical operators are located. Our findings are useful for the study of the one-electron and two-electron spectral weight distribution of physical operators.