  A superclimbing dislocation spread over several valleys of Peierls potential
in solid Helium-4 represents a non-Luttinger Liquid according to the elementary
scaling dimensional analysis because its excitation spectrum is parabolic.
Monte Carlo simulations, however, reveal that such a dislocation develops
Luttinger Liquid behavior, which can also undergo a transition into insulating
state. External bias can restore the parabolic spectrum. An experimental
verification of the effect is proposed.
