Functional theory of the spectral density via local embedding

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 a recently introduced 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.