Eur. Phys. J. B (2018) 91: 192
https://doi.org/10.1140/epjb/e2018-90277-3

Regular Article

Spectroscopy of the Hubbard dimer: the spectral potential^★

¹ European Theoretical Spectroscopy Facility (ETSF) and Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA, Université Paris-Saclay, 91128 Palaiseau, France
² Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France

^a e-mail: matteo.gatti@polytechnique.fr

Received: 23 April 2018
Received in final form: 13 June 2018
Published online: 30 August 2018

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.