Real space Mott-Anderson electron localization with long-range interactions: exact and approximate descriptions

TL;DR

This paper investigates how disorder and long-range interactions influence electron localization in a real-space 1D model, comparing exact solutions with density functional approximations to understand phase transitions.

Contribution

It provides a detailed analysis of localization mechanisms in real-space models with long-range Coulomb interactions, highlighting differences from lattice models and evaluating density functional methods.

Findings

Disorder induces a transition from metallic to insulating phases.

Single-particle occupation entropy effectively characterizes localization.

Density functional approximations show varying accuracy in reproducing exact densities.

Abstract

Real materials always contain, to some extent, randomness in the form of defects or irregularities. It is known since the seminal work of Anderson that randomness can drive a metallic phase to an insulating one, and the mechanism responsible for this transition is intrinsically different from the one of the interaction-induced transitions discovered by Mott. Lattice Hamiltonians, with their conceptual and computational advantages, permitted to investigate broadly the interplay of both mechanisms. However, a clear understanding of the differences (or not) with their real-space counterparts is lacking, especially in the presence of long-range Coulomb interactions. This work aims at shedding light on this challenging question by investigating a real-space one-dimensional model of interacting electrons in the presence of a disordered potential. The transition between delocalized and localized phases are characterized using two different indicators, namely the single-particle occupation entropy and the position-space information entropy. In addition, the performance of density functional approximations to reproduce the exact ground-state densities of this many-body localization model are gauged.