Exact and many-body perturbation solutions of the Hubbard model applied to linear chains

TL;DR

This paper compares the GW approximation with exact diagonalization for the Hubbard model in linear chains, showing GW improves energy, magnetization, and phase transition predictions over mean-field methods.

Contribution

It demonstrates the effectiveness of the GW approximation in capturing many-body effects in small Hubbard chains, extending its application beyond traditional mean-field approaches.

Findings

GW reduces total energy and magnetization compared to mean-field.

GW improves energy gap predictions, especially in even-numbered chains.

GW predicts a higher Hubbard parameter for phase transition than mean-field.

Abstract

This study examines how the GW approximation, one of the techniques covered by Green's functions and on many-body approximations (GFMBA), fares compared to the treatment of the Hubbard model solved using an exact diagonalization (ED) approach. We show that, for small linear chains, the GW approximation corrects the usual mean-field (MF) approach by reducing the total energy as well as the magnetization from the MF approximation. The energy gap shows also a better agreement with ED, especially in even-number of atoms systems where no plateau is observed below the predicted phase transition as in MF approximation. In terms of density of states, the GW approximation induces quasi-particles and side satellites peaks via a splitting process of MF peaks. At the same time, GW slightly changes the localization (e.g., edges or center) of the states. We also extend to GW approximation the L\"owdin's symmetry dilemma and show that GW predicts a paramagnetic-antiferromagnetic phase transition at a higher Hubbard parameter than MF.