Critical Hamiltonians on one‐dimensional disordered lattices

We focus on tight‐binding Hamiltonians on a regular one‐dimensional lattice with non‐random long‐range inter‐site coupling J mn = 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 Δ c . We claim that the invariance manifests the transition. We find that Δ c ≠ 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)