The first excited state of the asymmetric Hubbard dimer is not non-interacting v-representable, but becomes complex-v-representable via analytic continuation; state-specific Kohn-Sham calculations with approximate functionals can yield spurious stationary solutions.
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Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
The first excited state of the asymmetric Hubbard dimer is not non-interacting v-representable, but becomes complex-v-representable via analytic continuation; state-specific Kohn-Sham calculations with approximate functionals can yield spurious stationary solutions.