Comparison between the Bethe-Salpeter Equation and Configuration Interaction Approaches for Solving a Quantum Chemistry Problem: Calculating the Excitation Energy for Finite 1D Hubbard Chains

We calculate the excitation energies of finite 1D Hubbard chains with a variety of different site energies from two perspectives: (i) the physics-based Bethe-Salpeter equation (BSE) method and (ii) the chemistry-based configuration interaction (CI) approach. Results obtained from all methods are compared against the exact values for three classes of systems: metallic, impurity-doped, and molecular (semiconducting/insulating) systems. While in a previous study we showed that the GW method holds comparative advantages versus traditional quantum chemistry approaches for calculating the ionization potentials and electron affinities across a large range of Hamiltonians, we show now that the BSE method outperforms CI approaches only for metallic and semiconducting systems. For insulating molecular systems, CI approaches generate better results.