Localization of Two Interacting Particles in One-Dimensional Random Potential

Abstract

We investigate the localization of two interacting particles in one-dimensional random potential. Our definition of the two-particle localization length, $ξ$, is the same as that of v. Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)] and $ξ$'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, $ξ$ approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as $ξ\sim W^{-ν_0}$ for small $W$ with $ν_0 = 2.1 \pm 0.1$. When $U\neq 0$, we use the finite size scaling ansatz and find the relation $ξ\sim W^{-ν}$ with $ν= 2.9 \pm 0.2$. Moreover, data show the scaling behavior $ξ\sim W^{-ν_0} g(|U|/W^Δ)$ with $Δ= 4.0 \pm 0.5$.