Wave-Function Factorization of the Normal-Ordered 1D Hubbard Model for Finite Values of the On-site Repulsion U

TL;DR

This paper demonstrates that in the thermodynamic limit, the wave functions of excited states in the 1D Hubbard model factorize for all U, simplifying the analysis of spectral properties through a pseudofermion framework.

Contribution

It introduces a wave function factorization in the 1D Hubbard model and develops a pseudofermion operator algebra for analyzing finite-energy spectral properties.

Findings

Wave function factorizes for all U in the thermodynamic limit.

Pseudofermion description effectively captures finite-energy spectral features.

Pseudoparticle-pseudofermion transformation simplifies the model's analysis.

Abstract

In this paper we find that in the thermodynamic limit and for the the ground-state normal-ordered 1D Hubbard model the wave function of the excited energy eigenstates which span the Hilbert subspace where the finite-number-electron excitations are contained factorizes for all values of the on-site Coulombian repulsion U. This factorization results from the absence of residual energy interactions for the pseudofermions whose occupancy configurations describe these states. Our study includes the introduction of the pseudoparticle - pseudofermion unitary transformation and of an operator algebra for both the pseudoparticles and the pseudofermions. As the corresponding pseudoparticles, the $c\nu$ pseudofermions (and $s\nu$ pseudofermions) are $\eta$-spin zero $2\nu$-holon composite quantum objects (and spin zero $2\nu$-spinon composite quantum objects) where $\nu=1, 2,...$. The pseudofermion description is the most suitable for the study of the finite-energy spectral properties.