A symmetry-projected variational approach to the 1-dimensional Hubbard-model

TL;DR

This paper introduces a symmetry-projected variational method adapted from nuclear physics to accurately approximate energies, occupation numbers, and spectral functions of the 1D Hubbard model, matching exact solutions for various lattice sizes.

Contribution

It applies a symmetry-projected variational approach to the 1D Hubbard model, demonstrating accurate results for energies, occupation numbers, and spectral functions across different lattice sizes.

Findings

Accurately reproduces energies and occupation numbers for N=12 and N=14 lattices.

Provides good agreement with exact spectral functions.

Successfully extends to larger lattices like N=30.

Abstract

We apply a variational method devised for the nuclear many--body problem to the 1-dimensional Hubbard--model with nearest neighbor hopping and periodic boundary conditions. The test wave function consist for each state out of a single Hartree--Fock determinant mixing all the sites (or momenta) as well as the spin--projections of the electrons. Total spin and linear momentum are restored by projection methods before the variation. It is demonstrated that this approach reproduces the results of exact diagonalisations for half--filled N=12 and N=14 lattices not only for the energies and occupation numbers of the ground but also of the lowest excited states rather well. Furthermore, a system of 10 electrons in a N=12 lattice is investigated and, finally, a N=30 lattice is studied. In addition to energies and occupation numbers we present the spectral functions computed with the help of the symmetry--projected wave functions, too. Also here nice agreement with the exact results (where available) is reached.