Singular Behavior of Anderson Localized Wavefunctions for a Two-Site Model

Abstract

We show analytically that the apparent non-analyticity discovered recently in the inverse participation ratio (IPR) of the eigenstates in Anderson's model of localization is also present in a simple two-site model, along with a concurrent non-analyticity in the density of states (DOS) at the same energy. We demonstrate its evolution from two sites to the thermodynamic limit by numerical methods. For the two site model, non-analyticity in higher derivatives of the DOS and IPR is also proven to exist for all bounded distributions of disorder.

References in corpus (1)

• Singular Behavior of Eigenstates in Anderson's Model of Localization

Cited by in corpus (11)

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• Two-dimensional quantum percolation with binary non-zero hopping integrals
• Energy dependence of localization with interactions and disorder: The generalized inverse participation ratio of an ensemble of two-site Anderson-Hubbard systems
• Effect of Hilbert space truncation on Anderson localization
• Anderson localization at large disorder
• The scaling behaviour of localised and extended states in one-dimensional tight-binding models with disorder
• Strong-disorder renormalization group approach to the Anderson model using Raleigh-Schrödinger perturbation theory
• Persistence of energy-dependent localization in the Anderson-Hubbard model with increasing system size and doping
• Large Disorder Renormalization Group Study of the Anderson Model of Localization