In contrast, xBW2 only displays a marginal improvement over MP2. It is therefore not trivially the case that regularization allows applying MP2-like methods to metallic systems. Indeed, it is worth reemphasizing that MP2 diverges for finitesized HEG supercells, even though these do not display a vanishing band gap. Therefore, the simplistic notion that fixing MP2 in the ∆ ab i j → 0 limit is sufficient to describe metals is not correct. Instead, higher-order screening effects are essen-tial for describing uniform electron densities with or without gaps. These effects are apparently captured by the κ-MP2 regularizer to some extent, but not by xBW2. One-Dimensional Hubbard Model: Next, we investigate the performance of regularized MP2-like methods for the strongly correlated Hubbard model. The Hubbard model and related Hamiltonians were independently proposed in physics by Hubbard , Kanamori and Gutzwiller and in chemistry by Pariser, Parr and Pople . These model Hamiltonians cover the behaviour of a wide range of correlated systems such as high T c superconductivity , magnetism and the Mott metal-insulator transition .