Scaling in Interaction-Assisted Coherent Transport

TL;DR

This paper investigates how interactions between two electrons affect their localization length in disordered one-dimensional systems, revealing a scaling relationship with a specific exponent that clarifies previous discrepancies.

Contribution

The study provides a numerical analysis of the pair localization length scaling, introducing a refined scaling picture that accounts for wavefunction overlap distributions, differing from earlier estimates.

Findings

L_2 scales with L_1^{1.65}

The exponent differs from the previously estimated value of 2

A scaling picture explains the discrepancy using wavefunction overlap distributions

Abstract

The pair localization length $L_2$ of two interacting electrons in one--dimensional disordered systems is studied numerically. Using two direct approaches, we find $L_2 \propto L_1^{\alpha}$, where $L_1$ is the one-electron localization length and $\alpha \approx 1.65$. This demonstrates the enhancement effect proposed by Shepelyansky, but the value of $\alpha$ differs from previous estimates ($\alpha=2$) in the disorder range considered. We explain this discrepancy using a scaling picture recently introduced by Imry and taking into account a more accurate distribution than previously assumed for the overlap of one-electron wavefunctions.