Dimensional dependence of the metal-insulator transition

Abstract

We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3\le d\le 6$ disordered tight binding model with theoretical arguments. Our results indicate that, in agreement with the one parameter scaling theory, the upper critical dimension for localization is infinity. Typical properties of the spectral correlations at the Anderson transition such as level repulsion or a linear number variance are still present in higher dimensions though eigenvalues correlations get weaker as the dimensionality of the space increases. It is argued that such a critical behavior can be traced back to the exponential decay of the two-level correlation function in a certain range of eigenvalue separations. We also discuss to what extent different effective random matrix models proposed in the literature to describe the Anderson transition provide an accurate picture of this phenomenon. Finally, we study the effect of a random flux in our results.

RevTex4, 8 two-column pages, 5 .eps figures

References in corpus (3)

• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Multifractality of Hamiltonians with power-law transfer terms
• Critical level spacing distribution in long-range hopping Hamiltonians

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• Metallic phase of the quantum Hall effect in four-dimensional space
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Scale-invariant critical dynamics at eigenstate transitions
• Renormalization group for Anderson localization on high-dimensional lattices
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Borel-Padé re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes
• Localization and delocalization properties in quasi-periodically driven one-dimensional disordered system
• Interpretation of high-dimensional numerical results for Anderson transition
• Entanglement dynamics of monitored noninteracting fermions on graphics processing units
• Presence and Absence of Delocalization-localization Transition in Coherently Perturbed Disordered Lattices
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Critical Dynamics of the Anderson Transition on Small-World Graphs