Lieb-Wu Solution, Gutzwiller-Wave-Function, and Gutzwiller-Ansatz Approximation, with Adjustable Single-Particle Wave Function for the Hubbard Chain

TL;DR

This paper compares the exact Lieb-Wu solution with Gutzwiller-based approximations for the Hubbard chain, optimizing single-particle wave functions to analyze electronic properties as a function of interatomic distance.

Contribution

It introduces an approach that completes the Lieb-Wu solution by optimizing single-particle wave functions and compares various methods for the Hubbard chain.

Findings

Lieb-Wu solution provides exact electronic properties.

Gutzwiller approximations closely match the exact solution.

Optimized wave functions improve the description of the chain's properties.

Abstract

The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb - Wu exact solution (LW), the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatz case (GA). The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the Exact Diagonalization combined with an Ab Initio adjustment of the single-particle wave functions in the correlated state (EDABI method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controllable parameter - the interatomic distance.