Singular behavior of tight-binding chains with off-diagonal disorder

We prove that the density of states of the one-dimensional tight-binding Hamiltonian with off-diagonal disorder is singular at the center of the band, $E=0$, for every probability distribution of the hopping matrix elements V. The asymptotic form is ρ(E)2σ²|E(lnE²)|³, with σ²≡〈(lnV²)²〉-〈lnV²〉². The localization length goes to infinity as L(E)2|lnE²|σ². We also give a procedure to handle the problem numerically near the singularity, and we present some sample calculations.