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 λ 〈 2）, the spectrum-averaged concurrence N（C） first decreases slowly as A increases until its local minimum, then increases with λ until its peak at λ = 2, while for electrons in localized regimes （λ 〉 2）, N（C） decreases drastically as λ increases. The functions of N（C） versus λ are different for electrons in extended and localized regimes. The maximum of N（C） occurs at the point λ= 2, which is the critical value in the one-dimensional singleparticle 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 λ 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.
The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.
We numerically study the fidelity of an electron in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. Our results show that many properties of the two models can be well reflected by the fidelity： （i） the mobility edge and metal-insulator transition can be characterized by the static fidelity; （ii） the extended state and localized state can be identified by the dynamic fidelity. Therefore, it may broaden the applied areas of the fidelity.
