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Chinese Physics Letters

Entanglement in One-Dimensional Anderson Model with Long-Range Correlated Disorder

Guo Zi-zheng

Published Mar 1, 2008• 4 citations
Publisher

Abstract

By using the measure of concurrence, the entanglement of the ground state in the one-dimensional Anderson model is studied with consideration of the long-range correlations. Three kinds of correlations are discussed. We compare the effects of the long-rang Gaussian and power-law correlations between the site energies on the concurrence, and demonstrate the existence of the band structure of the concurrence in the power-law case. The emergence of the sharp kink on the concurrence curve shown in the intraband or in the interband indicates the position at which the localization extent of the state may have the severe variation. We use the Rudin–Shapiro model to describe the site energy distribution of the nucleotides of the DNA chain: guanine (G), adenine (A), cytosine(C), thymine (T). This model is a tetradic quasiperiodic sequence and is shown to be long-range correlated. Our results show that correlations between the site energies increase the concurrences.

DOI
10.1088/0256-307x/25/3/074

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By using the measure of concurrence, the entanglement of the ground state in the one-dimensional Anderson model is studied with consideration of the long-range correlations. Three kinds of correlations are discussed. We compare the effects of the long-rang Gaussian and power-law correlations between the site energies on the concurrence, and demonstrate the existence of the band structure of the concurrence in the power-law case. The emergence of the sharp kink on the concurrence curve shown in the intraband or in the interband indicates the position at which the localization extent of the state may have the severe variation. We use the Rudin–Shapiro model to describe the site energy distribution of the nucleotides of the DNA chain: guanine (G), adenine (A), cytosine(C), thymine (T). This model is a tetradic quasiperiodic sequence and is shown to be long-range correlated. Our results show that correlations between the site energies increase the concurrences.
The ground state entanglement in one- and two-dimensional Anderson models are studied with consideration of the long-range correlation effects and using the measures of concurrence and von Neumann entropy. We compare the effects of the long-range power-law correlation for the on-site energies on entanglement with the uncorrelated cases. We demonstrate the existence of the band structure of the entanglement. The intraband and interband jumping phenomena of the entanglement are also reported and explained to as the localization-delocalization transition of the system. We also demonstrated the difference between the results of one- and two-dimensions. Our results show that the correlation of the on-site energies increases the entanglement.
The effects of long-range power-law correlation on the intrinsic energy,intrinsic wave function and entanglement of one-dimensional disorder system were studied,and the changes of localization were observed.The results show that the entanglement of the three measures is fully enough to reflect the properties of correlation.As an example of correlation,the entanglement of DNA molecular chain was studied using the Anderson model.The results show that the entanglement has similar properties with the correlation and reflects the properties of the correlation.
由使用同时发生的措施，在一个维的安德森模型的扎根的状态的纠纷与远程的关联的考虑被学习。三种关联被讨论。我们在同时发生上比较在地点精力之间的长戒指的 Gaussian 和幂定律关联的效果，并且在幂定律盒子中表明同时发生的乐队结构的存在。在 intraband 或在显示出的同时发生曲线上的锋利的纽结的出现内部乐队显示状态的本地化程度可以在有严重变化的位置。我们使用 Rudin-Shapiro 模型描述 DNA 链的核苷酸的地点精力分发：guanine (G) ，腺嘌(A) ， cytosine (C) ，胸腺嘧啶(T) 。这个模型是 tetradic 伪周期的顺序并且被显示远程相关。我们的结果证明在地点精力之间的关联增加同时发生。
The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.
We consider the one-dimensional (1D) quasiperiodic Anderson-lattice model, which has quasiperiodically ordered impurities. The sites with an f-orbital are ordered as a “Fibonacci word”, one way to form 1D quasiperiodic orderings. To treat the correlation effect precisely, we use the density matrix renormalization group (DMRG) method. We show that the spin correlation function in the quasiperiodic system gives a characteristic pattern. Also, by analyzing the f-electron number and its fluctuation, we find that a valence transition, which usually occurs in the periodic Anderson model when the on-site interorbital interaction is large, is not sharp in the quasiperiodic system. Finally, we discuss the properties of the quasiperiodic Anderson-lattice model, comparing them against the Anderson-lattice model with randomly located f-orbitals. We find that the quasiperiodic Anderson-lattice model has a similar property to the periodic Anderson model for spin correlation, but also has a similar property to the Anderson-lattice model with randomly located f-orbitals for the valence fluctuation.