Emergence of Luttinger Liquid behavior of a superclimbing dislocation

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.