Normal-Ordered Wave-Function Factorization of the 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 on-site repulsion values, due to the non-interacting pseudofermions.

Contribution

It introduces a wave-function factorization for the 1D Hubbard model's excited states and develops a pseudofermion operator algebra and transformation.

Findings

Wave function factorization for all U values

Pseudofermions are non-interacting with no residual interactions

Introduction of a pseudoparticle-pseudofermion transformation

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 excited states contained in few-electron excitations factorizes for all values of the on-site Coulombian repulsion. This factorization results from the non-interacting character of the pseudofermions whose occupancy configurations describe these excited states. Our study includes the introduction of the pseudoparticle - pseudofermion unitary transformation and of an operator algebra for both the pseudoparticles and the pseudofermions. The pseudofermions are non interacting and thus have no residual interactions, in contrast to the corresponding pseudoparticles, whose statistics we classify according to the generalized Pauli principle. The physics behind the invariance of the pseudoparticles under the above transformations for specific values of the bare momentum is also studied and discussed.