Abstract

We address the problem of interacting electrons in an external potential by introducing the occupied 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 that embeds it into an open quantum system. Then, we use the Klein functional to define a universal functional of the spectral density, introduce a variational principle for the total energy, and formulate a non-interacting mapping suitable for numerical applications. The resulting equations, which involve local and dynamical potentials, are then solved by using the algorithmic inversion method based on a sum-over-poles to represent propagators. At variance with time-dependent density-functional theory, this formulation aims at studying charged excitations and electronic spectra with a functional theory, although possibly leading to accurate approximations for the total energy.