TITLE: Functional theory of the spectral density via local embedding

AUTHORS: A. Ferretti, T. Chiarotti, N. Marzari

AFFILIATIONS:
1. Centro S3, CNR–Istituto Nanoscienze, 41125 Modena, Italy
2. Theory and Simulations of Materials (THEOS) and National Centre for
   Computational Design and Discovery of Novel Materials (MARVEL),
    ́Ecole Polytechnique F ́ed ́erale de Lausanne, 1015 Lausanne, Switzerland

BODY:
We address the problem of interacting electrons in an external potential
by introducing the local spectral density as fundamental variable. 
First we formulate the problem using an embedding framework and prove 
a one-to-one correspondence between a spectral density and the local, 
dynamical external potential playing the role of embedding self-energy.
Then, we use the Klein functional to (i) define a universal functional 
of the spectral density, (ii) introduce a variational principle for 
the total energy, and (iii) formulate a non-interacting mapping suitable 
for numerical applications.

We adopt a sum-over-poles representation for the propagators 
combined with an algorithmic inversion method which allow us to
efficiently solve the Dyson equations (involving dynamical potentials) arising from
the above formulation.

At variance with time-dependent density-functional theory, this formulation 
aims at studying charged excitations with a functional theory, and, 
given the more informative content of the spectral density, 
can also lead to more accurate approximations for the total energy.