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

TL;DR

This paper uses von Neumann entropy to numerically analyze the localization properties of two interacting particles in various one-dimensional systems, revealing how entropy varies with interaction strength and different regimes.

Contribution

It introduces von Neumann entropy as a tool to characterize localization in two-particle systems across disordered, quasiperiodic, and slowly varying potentials, clarifying previous discrepancies.

Findings

Entropy peaks at intermediate interaction strengths.

Different entropy behaviors in extended and localized regimes.

Entropy effectively characterizes localization properties.

Abstract

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.