Dielectric response of the interacting 1D spinless fermions with disorder

TL;DR

This paper numerically investigates the dielectric response of one-dimensional disordered and interacting spinless fermion systems, revealing step-like behaviors and analyzing metal-insulator transitions through scaling.

Contribution

It extends DMRG methods to nonuniform systems and provides new insights into dielectric responses and phase diagrams of disordered interacting fermions.

Findings

Step-like dielectric response curves indicating breakdowns.

Generation of kink-pairs in Mott insulators causes steps.

Level crossings in Anderson insulators cause steps.

Abstract

Dielectric responces of the one-dimentional electron system is investigated numerically. We treat an interacting one-dimentional spinless fermion model with disorder by using the Density Matrix Renormalization Group(DMRG) method which is extended for nonuniform systems. We apply an electric field $E$ to the system and calculate dielectric responces. Dielectric responce of the Mott insulator and the Anderson insulator are calculated respectively. Steplike behaviors in $P-E$ curve are obtained which corresponds to breakdown of the insulating behavior. For the Mott insulator, the steps originate from generation of kink-pairs. For the Anderson insulator on the other hand, the origin of the steps is a crossing of the localized one particle energy levels. We also treat random systems with interaction. From one parameter scaling analysis of the susceptibility $\chi$, the metal-insulator transition in attractively interacting region is confirmed and a phase diagram of the random spinless fermion model is obtained.