  We consider the totally asymmetric simple exclusion process (TASEP) on the
periodic chain in the presence of a single impurity site that is inaccessible
to other particles and therefore acts as a static defect. Particles are allowed
to advance any distance l \geq 1 on the right with the probability that decays
as l^-(1+sigma), where sigma > 1. Despite the long range of hopping, we find
the same type of phase transition that occurs in the standard short-range TASEP
with a defect site where defect induces a macroscopic shock in the stationary
state. In particular, our model displays two main features characteristic of
the short-range TASEP with defect site: a growth of the shock width with system
size L as L^(1/2) or L^(1/3), depending on the existence of the particle-hole
symmetry, and the power-law decay in density profiles of the shock phase.
However, unlike the profiles in the short-range case, we find that the latter
are well reproduced by the mean-field approximation, which enables us to derive
the analytical expression for sigma-dependent exponent nu = sigma-1 of this
power-law decay and the point sigma_c = 4/3 at which the transition takes
place.
