physica status solidi (b)

Critical Hamiltonians on one‐dimensional disordered lattices

A. V. Malyshev, Francisco Domínguez-Adame, Viktor A. Malyshev

Published Jul 8, 2004• 1 citation

Abstract

Abstract We focus on tight‐binding Hamiltonians on a regular one‐dimensional lattice with non‐random long‐range inter‐site coupling Jmn = J/|m−n|μ and random uncorrelated site energies. Within the model the localization‐delocalization transition occurs at one of the energy band edges provided 1 < μ < 3/2. Using the model we demonstrate that the ratio of the first two momenta of the participation number distribution for the critical states is a size invariant parameter at some value of the disorder magnitude Δc. We claim that the invariance manifests the transition. We find that Δc ≠ 0 at 1 < μ < 3/2, suggesting that the system undergoes the localization‐delocalization transition with respect to disorder magnitude. At μ ≥ 3/2, all states are localized. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI: 10.1002/pssb.200304868

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