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 ${\rho }_s\sim T$ and sound velocity $v_s\sim T^{1\mathrm{/}2}$, showing similar unconventional low-temperature slow dynamics to the symmetry-broken regime. Particularly, the superfluid stiffness suggests an order by disorder effect as ${\rho }_s$ increases with temperature. Our results pave the way for studying fractons in ultracold atom experiments.