International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
Density and kinetic energy density -to- potential mapping on a latticeIris Theophilou
Max Planck Institute for Structure and Dynamics of Matter, Hamburg, Germany
Coauthor(s) : M. Ruggenthaler, F. Bucholz, F.G. Eich and A. Rubio[1,2]
 Universidad del Pais Vasco UPV/EHU, San Sebastian, Spain.
In the simple two-site Hubbard model one cannot reproduce the ground state 1-body Reduced Density Matrix (1-RDM) of the interacting system by a non-interacting one, even with non-local potentials and/or with some artificial temperature (grand canonical ensemble). Motivated from this fact, we show that in a lattice model we can reconstruct any density and kinetic energy density with properly adjusted potentials (local and non-local) of a fictitious non-interacting Hamiltonian. We achieve this by solving a system of non linear equations resulting from the steady state equations of motion of the fictitious system, which for a given density and kinetic energy density reproduce the functionals of the local and non-local potentials.