Density functional theory (DFT) in its practical implementations maps a system of interacting electrons onto an auxiliary noninteracting one and is presumably inaccurate for strongly correlated materials. We present a concrete benchmark for DFT by examining the electronic ground state phase diagram of a strongly interacting chain with uneven, noninteger nuclear charges. The interplay between charge imbalance and Coulomb repulsion yields two competing phases, a band insulator and a Mott insulator. By including infinitesimal lattice distortions, DFT stabilizes the intermediate spontaneously dimerized insulator phase that results from this competition. We assess the phase diagram by mapping the bond length and nuclear charge ratio of the chain to the ionic Hubbard model and performing highly accurate density matrix renormalization group calculations. Our comparative study provides foundational insight into the utility of symmetry-broken DFT as a predictive tool for elucidating phase diagrams with competing orders.

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• Landau theory
• Magnetic order
• Spontaneous symmetry breaking
• 1-dimensional systems
• Strongly correlated systems
• Density functional theory
• Density matrix renormalization group
• Hubbard model