Disorder Effects in Fluctuating One-Dimensional Interacting Systems

TL;DR

This paper investigates how fluctuations of a one-dimensional string influence the localization of interacting electrons in a disordered plane, revealing that string dynamics can enhance delocalization but do not alter the critical interaction strength unless the string is very soft.

Contribution

It introduces a perturbative renormalization group analysis of electron localization on fluctuating strings, highlighting the conditions under which string fluctuations affect the localization transition.

Findings

String fluctuations increase the delocalized regime.

Critical interaction strength remains unchanged unless the string is very soft.

Impurities act as dynamical in the electron frame, reducing localization effects.

Abstract

The zero temperature localization of interacting electrons coupled to a two-dimensional quenched random potential, and constrained to move on a fluctuating one-dimensional string embedded in the disordered plane, is studied using a perturbative renormalization group approach. In the reference frame of the electrons the impurities are dynamical and their localizing effect is expected to decrease. We consider several models for the string dynamics and find that while the extent of the delocalized regime indeed grows with the degree of string fluctuations, the critical interaction strength, which determines the localization-delocalization transition for infinitesimal disorder,does not change unless the fluctuations are softer than those of a simple elastic string.