Ground State Properties Of The One-Dimensional Hubbard Model: Symmetry Projected Variational Wave Function Approach

TL;DR

This paper develops a symmetry-based variational wave function approach to study the ground state properties of the one-dimensional Hubbard model, capturing electron interactions and magnetic correlations.

Contribution

It introduces a symmetry-projected variational wave function method tailored for the 4-site Hubbard model, analyzing different interaction regimes.

Findings

Ground state energies approach -4t as U→0.

Wave functions are valid for positive and negative Coulomb interactions.

System shows antiferromagnetic correlations.

Abstract

We use the $C_{4v}$ symmetry group of the 4-site Hubbard model to construct a ground state variational wave function of two- and four interacting electrons. In the limit $U\rightarrow 0$, ground state energies of the two- and four interacting electrons system is of the order $-4t$. The variational wave function of the four interacting electrons obtained using the $B_1$ irreducible representation is valid for on-site Coulomb repulsion, while the one obtained using the $A_1$ representation is valid for negative values of the Coulomb interaction. The system exhibits antiferromagnetic correlations.