Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

TL;DR

This paper investigates how interactions influence the localization length of two particles in a one-dimensional disordered system, revealing an interaction-dependent enhancement and providing detailed numerical analysis.

Contribution

The study introduces a decimation method to compute the two-particle localization length and demonstrates how it scales with interaction strength and disorder, extending understanding of TIP localization.

Findings

Localization length increases with interaction strength U.

Scaling exponent β(U) varies between 1 and 1.5.

Method reproduces known results for 2D Anderson model.

Abstract

We present calculations of the localisation length, $\lambda_{2}$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. $\lambda_{2}(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates $\xi_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite $U$, we find that $ \xi_{2}(U) \sim \xi_2(0)^{\beta(U)} $ with $\beta(U)$ varying between $\beta(0)=1$ and $\beta(1) \approx 1.5$. We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction.