Localization of Two Interacting Particles in One-Dimensional Random Potential

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 $\Delta = 4.0 \pm 0.5$.