Localization of Two Interacting Particles in One-Dimensional Random Potential

TL;DR

This paper studies how two interacting particles become localized in a one-dimensional random potential, revealing how their localization length depends on disorder strength and interaction, with new scaling relations identified.

Contribution

It introduces a finite size scaling approach to analyze the localization length of two interacting particles, establishing new scaling laws involving disorder and interaction strength.

Findings

Localization length scales as W^{-2.1} for U=0

Interaction modifies the scaling to W^{-2.9}

Scaling behavior includes a universal function g with a specific exponent

Abstract

We investigate the localization of two interacting particles in one-dimensional random potential. Our definition of the two-particle localization length, $\xi$, is the same as that of v. Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)] and $\xi$'s for chains of finite lengths are calculated numerically using the recursive Green's function method for several values of the strength of the disorder, $W$, and the strength of interaction, $U$. When U=0, $\xi$ approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as $\xi \sim W^{-\nu_0}$ for small $W$ with $\nu_0 = 2.1 \pm 0.1$. When $U\neq 0$, we use the finite size scaling ansatz and find the relation $\xi \sim W^{-\nu}$ with $\nu = 2.9 \pm 0.2$. Moreover, data show the scaling behavior $\xi \sim W^{-\nu_0} g(|U|/W^\Delta)$ with $\Delta = 4.0 \pm 0.5$.