  We present a one-dimensional nonlocal hopping model with exclusion on a ring.
The model is related to the Raise and Peel growth model. A nonnegative
parameter $u$ controls the ratio of the local backwards and nonlocal forwards
hopping rates. The phase diagram and consequently the values of the current,
depend on $u$ and the density of particles. In the special case of half-filling
and $u = 1$ the system is conformal invariant and an exact value of the current
for any size $L$ of the system is conjectured and checked for large lattice
sizes in Monte Carlo simulations. For $u > 1$ the current has a non-analytic
dependence on the density when the latter approaches the half-filling value.
