Characterizing localization properties of two spinless electrons in a one-dimensional Harper model with concurrence
Gong Long-Yan(巩龙)a)b)c) and Tong Pei-Qing(童培庆)b)†
a Department of Mathematics, Nanjing Normal University, Nanjing 210097, China; b Department of Physics, Nanjing Normal University, Nanjing 210097, China; c Department of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
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.
Received: 14 May 2007
Revised: 29 June 2007
Accepted manuscript online:
Fund: Project
supported by the National Nature Science Foundation of China (Grant
Nos 90203009, 10175035 and 10674072), by the Specialized Research
Fund for the Doctoral Program of Higher Education (Grant No
20060319007), by the Excellent Young Teacher Program of the Ministry
of Education of China, by the Nature Science Foundation of Jiangsu
Province of China (Grant No 06KJD140135).
Cite this article:
Gong Long-Yan(巩龙) and Tong Pei-Qing(童培庆) Characterizing localization properties of two spinless electrons in a one-dimensional Harper model with concurrence 2008 Chin. Phys. B 17 674
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