A simple position operator for periodic systems

Emília Valença Ferreira de Aragão (1, 2) , Diego Moreno (1, 2) , Stefano Battaglia (1, 3, 2) , Gian Luigi Bendazzoli (4) , Stefano Evangelisti (1, 2) , Thierry Leininger (2, 1) , Nicolas Suaud (5, 2) , Arjan Berger (1, 6, 2)

1 GMO - Groupe THEO (LCPQ)
2 LCPQ - Laboratoire de Chimie et Physique Quantiques
3 UNIPG - Università degli Studi di Perugia = University of Perugia
4 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
5 SEM - Systèmes étendus et magnétisme (LCPQ)
6 ETSF - European Theoretical Spectroscopy Facility

We present a position operator that is compatible with periodic boundary conditions (PBC). It is a one-body operator that can be applied in calculations of correlated materials by simply replacing the traditional position vector by the new definition. We show that it satisfies important fundamental as well as practical constraints. To illustrate the usefulness of the PBC position operator we apply it to the localization tensor, a key quantity that is able to differentiate metallic from insulating states. In particular, we show that the localization tensor given in terms of the PBC position operator yields the correct expression in the thermodynamic limit. Moreover, we show that it correctly distinguishes between finite precursors of metals and insulators.

Domaines: Autre [cond-mat.other]

Emília Valença Ferreira de Aragão, Diego Moreno, Stefano Battaglia, Gian Luigi Bendazzoli, Stefano Evangelisti, et al.. A simple position operator for periodic systems. Physical Review B, 2019, 99 (20), pp.205144. ⟨10.1103/PhysRevB.99.205144⟩. ⟨hal-02155386⟩