Functional theory of the occupied spectral density

TL;DR

This paper introduces a new functional theory based on the occupied spectral density to better understand electronic spectra and correlations in interacting electron systems, offering a potential improvement over existing methods.

Contribution

It formulates a spectral density functional theory with a variational principle and a non-interacting mapping, advancing the study of electronic excitations and correlations.

Findings

Established a one-to-one correspondence between spectral density and local potential.

Defined a universal functional of the spectral density using Klein functional.

Proposed a variational principle and spectral self-consistent equations for numerical applications.

Abstract

We address the problem of interacting electrons in an external potential by introducing the occupied spectral density $\rho(\mathbf{r},\omega)$ as fundamental variable. First, we formulate the problem using an embedding framework, and prove a one-to-one correspondence between a $\rho(\mathbf{r},\omega)$ and the local dynamical external potential $v_{\text{ext}}(\mathbf{r},\omega)$ that embeds the interacting electrons into an open quantum system. Then, we use the Klein functional to ($i$) define a universal functional of $\rho(\mathbf{r},\omega)$, ($ii$) introduce a variational principle for the total energy as a functional of $\rho(\mathbf{r},\omega)$, and ($iii$) formulate a non-interacting mapping of spectral self-consistent equations suitable for numerical applications. At variance with time-dependent density-functional theory, this formulation aims at studying charged excitations and electronic spectra -- including electronic correlations -- with a functional theory; An explicit and formally correct description of all electronic levels could also lead to more accurate approximations for the total energy.