Energy-level statistics at the metal-insulator transition in anisotropic systems

TL;DR

This study investigates the Anderson model with anisotropic hopping to understand how anisotropy affects the metal-insulator transition, critical disorder, and energy-level statistics, providing new insights into anisotropic localization phenomena.

Contribution

It offers the first detailed numerical analysis of the Anderson transition in anisotropic systems, including critical disorder, exponent, and level statistics behavior.

Findings

Critical disorder decreases with anisotropy following a power law.

Critical exponent remains consistent with isotropic models.

Level statistics evolve from isotropic form to Poisson with increased anisotropy.

Abstract

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e. weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition using energy-level statistics. The values of the critical disorder $W_c$ are consistent with results of previous studies, including the transfer-matrix method and multifractal analysis of the wave functions. $W_c$ decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent $\nu=1.45\pm0.2$. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. The critical level statistics which is independent of the system size at the transition changes from its isotropic form towards the Poisson statistics with increasing anisotropy.