Competition between the Mott transition and the Anderson localization in 1D disordered interacting electron systems

TL;DR

This paper investigates how strong disorder and electron interactions compete in one-dimensional systems, revealing conditions under which Mott insulators or Anderson localization dominate, using bosonization and renormalization group techniques.

Contribution

It provides a detailed analysis of the interplay between Mott transition and Anderson localization in 1D systems, including second-order beta function calculations with a replica trick.

Findings

Strong forward scattering destroys the Mott gap.

Backward scattering induces Anderson localization in gapless states.

Strong Umklapp interaction maintains Mott insulating behavior.

Abstract

The competition between the Mott transition and the Anderson localization in one dimensional electron systems is studied based upon the bosonization and the renormalization group method. The beta function is calculated up to the second order in the strength of diagonal disorder by using a replica trick. It is found that the sufficiently strong forward scattering by random impurities destroys the Mott-Hubbard gap, and the backward scattering gives rise to the Anderson localization for the resulting gapless state. On the other hand, if the Umklapp interaction is strong enough, the Mott insulating state still overwhelms the Anderson localization.