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Exactly solvable model with two conductor-insulator transitions driven by impurities.

Abstract

We present an exact analysis of two conductor-insulator transitions in the random graph model where low connectivity means high impurity concentration. The adjacency matrix of the random graph is used as a hopping Hamiltonian. We compute the height of the delta peak at zero energy in its spectrum exactly and describe analytically the structure and contribution of localized eigenvectors. The system is a conductor for average connectivities between 1.421 529ellipsis and 3.154 985ellipsis but an insulator in the other regimes. We explain the spectral singularity at average connectivity e = 2.718 281ellipsis and relate it to other enumerative problems in random graph theory.

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BibTeXRIS

M Bauer, O Golinelli. 2001-03-19. Exactly solvable model with two conductor-insulator transitions driven by impurities.. https://doi.org/10.1103/physrevlett.86.2621

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