Anderson Localization and Polarization

TL;DR

This paper explores the effects of randomness and electron interactions on localization in one-dimensional systems using DMRG, aiming to extend understanding of Anderson localization to correlated electrons.

Contribution

It introduces a numerical approach applying DMRG to study both randomness and electron interactions in 1D systems, filling a gap in existing research.

Findings

Analysis of non-interacting random systems

Extension of DMRG to correlated disordered systems

Insights into localization phenomena with interactions

Abstract

Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson localization. Although we have well established understanding of the localization of non-interacting electrons, information of the correlated electrons with randomness is still missing. It was mainly due to lack of reliable numerical techniques for the correlated electrons. For the one dimensional correlated systems without randomness, lots of numerical results are collected by the Density Matrix Renormalization Group (DMRG) method and consistent understanding with analytical predictions has been achieved. In this paper, we plan to apply DMRG for the random electron systems by calculating direct responses of the system with electric field. At first, random systems without interaction are carefully investigated. Then we try to treat both of interaction and randomness in one dimensional systems.