von Neumann entropy and localization properties of two interacting particles in one-dimensional nonuniform systems

With the help of von Neumann entropy, we study numerically the localization properties of two interacting particles (TIP) with on-site interactions in one-dimensional disordered, quasiperiodic, and slowly varying potential systems, respectively. We find that for TIP in disordered and slowly varying potential systems, the spectrum-averaged von Neumann entropy < E-v > first increases with interaction U until its peak, then decreases as U gets larger. For TIP in the Harper model [S. N. Evangelou and D. E. Katsanos, Phys. Rev. B 56, 12797 (1997)], the functions of < E-v > versus U are different for particles in extended and localized regimes. Our numerical results indicate that for these two-particle systems, the von Neumann entropy is a suitable quantity to characterize the localization properties of particle states. Moreover, our studies propose a consistent interpretation of the discrepancies between previous numerical results.