  We construct exact ground states of interacting electrons on triangle and
diamond Hubbard chains. The construction requires (i) a rewriting of the
Hamiltonian into positive semidefinite form, (ii) the construction of a
many-electron ground state of this Hamiltonian, and (iii) the proof of the
uniqueness of the ground state. This approach works in any dimension, requires
no integrability of the model, and only demands sufficiently many microscopic
parameters in the Hamiltonian which have to fulfill certain relations. The
scheme is first employed to construct exact ground state for the diamond
Hubbard chain in a magnetic field. These ground states are found to exhibit a
wide range of properties such as flat-band ferromagnetism and correlation
induced metallic, half-metallic or insulating behavior, which can be tuned by
changing the magnetic flux, local potentials, or electron density. Detailed
proofs of the uniqueness of the ground states are presented. By the same
technique exact ground states are constructed for triangle Hubbard chains and a
one-dimensional periodic Anderson model with nearest-neighbor hybridization.
They permit direct comparison with results obtained by variational techniques
for f-electron ferromagnetism due to a flat band in CeRh3B2.
