Approximation to an exchange-correlation functional on the basis of renormalizatio-group theory*

Approximations to the exchange-correlation functional are central to Density Functional Theory. Generalizations of the Local-Density Approximation typically describe electronic systems very well. Nonetheless, many exceptions are known. The molecular junction offers an outstanding example, one in which nonlocal correlations stem from the Kondo effect. The junction comprises two metallic leads bridged by a molecule. At low temperatures, the molecular-orbital spin and the low-energy conduction-electron spins lock into a singlet, a entangled state that renders local approximations inadequate, so large is its diameter. To take a nonlocal approach, we resort to renormalization-group concepts. As the temperature T is reduced, the junction crosses over from the vicinity of a high-T fixed point, in which the molecular spin and lead electrons are decoupled, to a low-T fixed point, in which they are strongly coupled. The high-T fixed point is devoid of entanglement, hence well described by local approximations. We can therefore set up and solve the Kohn-Sham equations for that fixed point. We then combine the resulting Kohn-Sham eigenstates with the molecular spin to define a single-impurity Anderson Hamiltonian. Numerical renormalization-group diagonalization of the latter depicts the crossover to the low-T fixed point and yields the ground-state and temperature-dependent zero-bias transport properties of the junction. As an illustration, results for an inhomogeneous Hubbard model will be presented and compared with experimental data.