  The one-dimensional (1D) tight binding model with random nearest neighbor
hopping is known to have a singularity of the density of states and of the
localization length at the band center. We study numerically the effects of
random long range (power-law) hopping with an ensemble averaged magnitude
$\expectation{|t_{ij}|} \propto |i-j|^{-\sigma}$ in the 1D chain, while
maintaining the particle-hole symmetry present in the nearest neighbor model.
We find, in agreement with results of position space renormalization group
techniques applied to the random XY spin chain with power-law interactions,
that there is a change of behavior when the power-law exponent $\sigma$ becomes
smaller than 2.
