  The main candidate for the superfluid pathways in solid Helium-4 are
dislocations with Burgers vector along the hcp symmetry axis. Here we focus on
quantum behavior of a generic edge dislocation which can perform superclimb --
climb supported by the superflow along its core. The role of the long range
elastic interactions between jogs is addressed by Monte Carlo simulations. It
is found that such interactions do not change qualitatively the phase diagram
found without accounting for such forces. Their main effect consists of
renormalizing the effective scale determining compressibility of the
dislocation in the Tomonaga-Luttinger Liquid phase. It is also found that the
quantum rough phase of the dislocation can be well described within the
gaussian approximation which features off-diagonal long range order in 1D for
the superfluid order parameter along the core.
