Localization and Eigenvalue Statistics for the Lattice Anderson model with Discrete Disorder

Abstract

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.

46 pages, 1 figure. v4: minor changes, final version to appear in Reviews in Mathematical Physics

References in corpus (3)

• Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principle
• A discrete harmonic function bounded on a large portion of ${\mathbb{Z}}^2$ is constant
• On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder

Cited by in corpus (4)

• Time evolution of many-body localized systems in two spatial dimensions
• Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principle
• Quantum engineering for compactly localized states in disordered Lieb lattices
• Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice