Characterizing localization properties of two spinless electrons in a one-dimensional Harper model with concurrence

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.