Multifractal analysis of the metal-insulator transition in anisotropic systems
Multifractal analysis of the metal-insulator transition in anisotropic systems
复制标题
各向异性系统中金属-绝缘体转变的多重分形分析
DOI：
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发表时间：
1996
期刊：
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通讯作者：
M. Schreiber
中科院分区：
文献类型：
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作者：
F. Milde;R. A. Romer;M. Schreiber
我们研究了弱耦合链和弱耦合平面在三维情况下具有各向异性跳跃的安德森局域化模型。对于尺寸高达\(48^{3}\)的系统，通过兰索斯对角化计算得到的哈密顿量的本征态，即使在强各向异性的情况下，在金属 - 绝缘体转变处也表现出多重分形行为。从奇异谱的系统尺寸依赖性确定的临界无序强度\(W_{c}\)与最近使用转移矩阵方法的一项研究结果合理相符。但是在\(W_{c}\)处的相应谱偏离了为各向同性系统确定的“特征谱”。这表明与各向同性系统相比，各向异性系统状态的多重分形性质存在定量差异。此外，我们通过精确对角化计算了给定各向异性下的久保电导率。对于仅有\(12^{3}\)个格点的小系统尺寸，我们已经观察到，如果耦合变弱，在跳跃减小的方向上电导率会迅速下降。
We study the Anderson model of localization with anisotropic hopping in three dimensions for weakly coupled chains and weakly coupled planes. The eigenstates of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes up to ${48}^{3}$, show multifractal behavior at the metal-insulator transition even for strong anisotropy. The critical disorder strength ${\mathrm{W}}_{\mathrm{c}}$ determined from the system-size dependence of the singularity spectra is in a reasonable agreement with a recent study using transfer-matrix methods. But the respective spectrum at ${\mathrm{W}}_{\mathrm{c}}$ deviates from the ``characteristic spectrum'' determined for the isotropic system. This indicates a quantitative difference of the multifractal properties of states of the anisotropic as compared to the isotropic system. Further, we calculate the Kubo conductivity for given anisotropies by exact diagonalization. Already for small system sizes of only ${12}^{3}$ sites we observe a rapidly decreasing conductivity in the directions with reduced hopping if the coupling becomes weaker.