Spectroscopy of the Hubbard dimer: the spectral potential

TL;DR

This paper explores the spectral potential in the Hubbard dimer model, proposing an approximation strategy that uses the homogeneous limit and a connector approach, providing insights into its effectiveness and challenges.

Contribution

It introduces a novel approximation method for the spectral potential using the homogeneous limit and connector strategy, tested on the asymmetric Hubbard dimer.

Findings

The connector strategy offers promising results but has limitations in capturing all inhomogeneity effects.

Different approximation levels show varying degrees of accuracy compared to the exact solution.

Insights gained could inform future applications to real materials.

Abstract

The spectral potential is the dynamical generalization of the Kohn-Sham potential. It targets, in principle exactly, the spectral function in addition to the electronic density. Here we examine the spectral potential in one of the simplest solvable models exhibiting a non-trivial interplay between electron-electron interaction and inhomogeneity, namely the asymmetric Hubbard dimer. We discuss a general strategy to introduce approximations, which consists in calculating the spectral potential in the homogeneous limit (here represented by the symmetric Hubbard dimer) and importing it in the real inhomogeneous system through a suitable "connector". The comparison of different levels of approximation to the spectral potential with the exact solution of the asymmetric Hubbard dimer gives insights about the advantages and the difficulties of this connector strategy for applications in real materials.