Emergent dipole moment conservation and subdiffusion in tilted chains

We study transport in an interacting tilted (Stark) chain. We show that the crossover between diffusive and subdiffusive relaxation is governed by FL, where F is the strength of the field, and L is the wavelength of the excitation. While the subdiffusive behavior persists for large fields, the corresponding transport coefficient is exponentially suppressed with F so that the finite-time dynamics appears almost frozen. We (i) explain the crossover scale between the diffusive and subdiffusive transport by bounding the dynamics of the dipole moment for arbitrary initial state, (ii) prove its emergent conservation at infinite temperature for F1/L, and (iii) argue that the numerical data for the tilted chain are consistent with the hydrodynamics of fractons.