  The spectral potential is the dynamical generalization of the Kohn-Sham
potential. It targets, in principle exactly, the spectral function in addition
to the electronic density. Here we examine the spectral potential in one of the
simplest solvable models exhibiting a non-trivial interplay between
electron-electron interaction and inhomogeneity, namely the asymmetric Hubbard
dimer. We discuss a general strategy to introduce approximations, which
consists in calculating the spectral potential in the homogeneous limit (here
represented by the symmetric Hubbard dimer) and importing it in the real
inhomogeneous system through a suitable "connector". The comparison of
different levels of approximation to the spectral potential with the exact
solution of the asymmetric Hubbard dimer gives insights about the advantages
and the difficulties of this connector strategy for applications in real
materials.
