Electron Localization in the Insulating State

TL;DR

This paper provides a rigorous definition of electron localization in insulators, linking it to macroscopic polarization and demonstrating the concept through a one-dimensional Hubbard model.

Contribution

It introduces a precise formalism for electron localization in insulators and connects it to polarization, exemplified by a Hubbard model analysis.

Findings

Localization relates to Wannier orbital spread in noninteracting limit

Ground state sustains macroscopic polarization

Formalism applies to one-dimensional Hubbard model

Abstract

The insulating state of matter is characterized by the excitation spectrum, but also by qualitative features of the electronic ground state. The insulating ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is localized. We give a sharp definition of the latter concept, and we show how the two basic features stem from essentially the same formalism. Our approach to localization is exemplified by means of a two--band Hubbard model in one dimension. In the noninteracting limit the wavefunction localization is measured by the spread of the Wannier orbitals.