一维长程关联无序系统的局域性

Localization in the one-dimensional systems with long-range correlated disorder

研究了在紧束缚近似下,由de Moura和Lyra提出的一维长程关联无序模型的局域性.分布在[-W/2,W/2]区间的格点位能,其关联函数〈εiεj〉的傅里叶变换满足S(k)∝k-α,其中关联强度α>0.利用participation ratio不仅证实了在α>2和W<4时,会出现一段连续的扩展态,而且验证了一维长程关联无序系统局域性是无序与关联相互竞争的结果.另外,inverse participation ratio的演化图还能够清楚地反映出系统的局域化程度随无序强度W和关联强度α的变化过程,尤其是在α<2时的情况.

In this paper, we investigate the localization in a tight-binding one-dimensional model with long-range correlated disorder, which was proposed by de Moura and Lyra. The diagonal on-site energies are distributed in [ - W/2, W/2] and the Fourier transform S （k） of the two-point correlation function （ εiεj ） satisfies S （k） ∝ k ^-α with α 〉 0. Using the participation ratio, we confirm that there is a finite range of extended eigenstates for α 〉 2 and W 〈 4, and validate that the localization of the 1-D disordered model with long-range correlation is determined by the competition between the disorder and correlation. Also, the evolution of the inverse participation ratio as a function of the disorder strength and the correlation strength reflects the changing of the localization of the system, especially in the case of α 〈 2.