One and Two-Electron Spectral Function Line Shapes in the Vicinity of the Upper-Hubbard Bands Lower Limit

TL;DR

This paper derives general expressions for few-electron spectral functions near the upper-Hubbard band lower limits in the 1D Hubbard model, revealing insights into finite-energy spectral properties of the quantum liquid.

Contribution

It introduces a novel method combining symmetries and a finite-energy holon-spinon description to analyze spectral functions near upper-Hubbard band edges.

Findings

Derived expressions for spectral functions near upper-Hubbard band limits

Applied scheme to one-electron, structure factor, and Cooper pair spectral functions

Provided insights into finite-energy spectral properties of 1D quantum liquids

Abstract

In this paper we derive general expressions for few-electron spectral functions of the one-dimensional Hubbard model for values of the excitation energy in the vicinity of the $M^{th}$ upper-Hubbard band lower limit. Here $M=1,2,...$ is the rotated-electron double occupation, which vanishes for the ground state and is a good quantum number for all values of the on-site Coulomb repulsion $U$. Our studies rely on a combination of symmetries of the model with a recent finite-energy holon and spinon description of the quantum problem. We apply our general scheme to the one-electron addition spectral function, dynamical structure factor, and spin singlet Cooper pair addition spectral function. Our results provide physically interesting information about the finite-energy spectral properties of the many-electron one-dimensional quantum liquid.