Exact Excited-State Functionals of the Asymmetric Hubbard Dimer.

ABSTRACT: The exact functionals associated with the (singlet) ground state and the two singlet excited states of the asymmetric Hubbard dimer at half-filling are calculated using both Levy's constrained search and Lieb's convex formulation. While the ground-state functional is, as is commonly known, a convex function with respect to the density, the functional associated with the doubly excited state is found to be concave. Also, because the density-potential mapping associated with the first excited state is noninvertible, its "functional" is a partial, multivalued function composed of one concave and one convex branch that correspond to two separate domains of the external potential. Remarkably, it is found that, although the one-to-one mapping between density and external potential may not apply

SUBMITTER: Giarrusso S 

PROVIDER: S-EPMC10561271 | biostudies-literature | 2023 Oct

REPOSITORIES: biostudies-literature