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 (E) 2{^2}{|E (ln{E^2) |}^3}, with ^2〈 (ln{V^2) }^2〉-〈ln{V^2〉}^2. The localization length goes to infinity as L (E) 2|lnE^{2|}{^2}. We also give a procedure to handle the problem numerically near the singularity, and we present some sample calculations.