Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid

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By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional ab initio LDA is based on a Fermi liquid (the electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported.