Constrained Motions and Slow Dynamics in One-Dimensional Bosons with Double-Well Dispersion.

We demonstrate slow dynamics and constrained motion of domain walls in one-dimensional (1D) interacting bosons with double-well dispersion. In the symmetry-broken regime, the domain-wall motion is "fractonlike"-a single domain wall cannot move freely, while two nearby domain walls can move collectively. Consequently, we find an Ohmic-like linear response and a vanishing superfluid stiffness, which are atypical for a Bose condensate in a 1D translation invariant closed quantum system. Near Lifshitz quantum critical point, we obtain superfluid stiffness ρ_{s}∼T and sound velocity v_{s}∼T^{1/2}, showing similar unconventional low-temperature slow dynamics to the symmetry-broken regime. Particularly, the superfluid stiffness suggests an order by disorder effect as ρ_{s} increases with temperature. Our results pave the way for studying fractons in ultracold atom experiments.