关键词: entanglement, two interacting particles, localization, Harper model

Abstract: By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with on-site interaction $U$ moving in the one-dimensional Harper model. Generally speaking, for electrons in extended regimes (potential parameter $\lambda<2$), the spectrum-averaged concurrence $N\langle C\rangle$ first decreases slowly as $\lambda$ increases until its local minimum, then increases with $\lambda$ until its peak at $\lambda=2$, while for electrons in localized regimes ($\lambda>2$), $N\langle C\rangle$ decreases drastically as $\lambda$ increases. The functions of $N\langle C\rangle$ versus $\lambda$ are different for electrons in extended and localized regimes. The maximum of $N\langle C\rangle$ occurs at the point $\lambda=2$, which is the critical value in the one-dimensional single-particle Harper model. From these studies it can distinguish extended, localized and critical regimes for the two-particle system. It is also found for the same $\lambda$ that the interaction $U$ always induce the decreases of concurrence, i.e., the concurrence can reflect the localization effect due to the interaction. All these provide us a new quantity to understand the localization properties of eigenstates of two interacting particles.

Key words: entanglement, two interacting particles, localization, Harper model