International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
Effective Hamiltonians in RDMFT and single particle propetiesNektarios Lathiotakis
In DFT, the electron density of any interacting particle system in the ground state is reproduced by an independent electron system, the Kohn Sham system. Thus KS theory, apart from leading to a system of single particle equations that are solved self-consistently, it offers a very useful single-particle description from which spectral properties like orbital energies, electronic bands and densities of states are routinely used to characterize physical systems and describe several phenomena. On the contrary, in RDMFT, there is no "default" single particle Hamiltonian like KS in DFT. Ionization energies, however, can be obtained by applying Extended Koopmans' theorem . There are several attempts to define effective Hamitlonians in RDMFT  with mainly two targets: (1) to minimize effectively the total energy in RDMFT which is a relatively complicated task and (2) to define a useful single particle picture. In the present talk, we review several Hamiltonian schemes that have been proposed for RDMFT. We focus on the local-RDMFT  in which the occupation numbers are given as usual by minimizing the energy functional but the natural orbitals are replaced by those orbitals that optimize the same energy functional under the constraint that they obey a single particle Schroedinger equation with a local potential. We present applications of local RDMFT  as well as recent ideas to improve its efficiency and performance . We also compare the effective potential of local RDMFT with that obtained by inverting the density of a full RDMFT minimization .
 M. M. Morrell, R. G. Parr, and M. Levy, J. Chem. Phys. 62 549 (1975).
 K. Pernal, Phys. Rev. Lett. 94 233002 (2005); M. Piris and J. M. Ugalde, J. Comput. Chem. 30 2078 (2009); T. Baldsiefen and E. K. U. Gross, Comput. Theor. Chem. 1003 114 (2013); S. Sharma, J. K. Dewhurst, S. Shallcross, and E. K. U. Gross, Phys. Rev. Lett. 110 116403 (2013).
 N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A 90 032511 (2014).
 N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, J. Chem. Phys. 141 164120 (2014); Iris Theophilou, Nektarios N. Lathiotakis, Nikitas I. Gidopoulos, Angel Rubio, Nicole Helbig, J. Chem. Phys. 143 054106 (2015).
 N. N. Lathiotakis, N. I. Gidopoulos, (to be published).
 Iris Theophilou, Nektarios N. Lathiotakis, (to be published).