Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms

TL;DR

This paper studies a two-dimensional disordered electron system with long-range power-law transfer terms, revealing a metal-insulator transition and critical properties through numerical level statistics and finite size scaling.

Contribution

It introduces a numerical analysis of a 2D disordered model with power-law transfer, identifying a metal-insulator transition and critical exponents.

Findings

Metal-insulator transition observed for orthogonal symmetry.

Correlation length exponent estimated as ν=2.6±0.15.

Critical eigenstates exhibit multifractal behavior.

Abstract

We investigate a disordered two-dimensional lattice model for noninteracting electrons with long-range power-law transfer terms and apply the method of level statistics for the calculation of the critical properties. The eigenvalues used are obtained numerically by direct diagonalization. We find a metal-insulator transition for a system with orthogonal symmetry. The exponent governing the divergence of the correlation length at the transition is extracted from a finite size scaling analysis and found to be $\nu=2.6\pm 0.15$. The critical eigenstates are also analyzed and the distribution of the generalized multifractal dimensions is extrapolated.