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We study the transport dynamics of an interacting tilted (Stark) chain. Weshow that the crossover between diffusive and subdiffusive dynamics is governedby $F\sqrt{L}$, where $F$ is the strength of the field, and $L$ is thewave-length of the excitation. While the subdiffusive dynamics persist forlarge fields, the corresponding transport coefficient is exponentiallysuppressed with $F$ so that the finite-time dynamics appear almost frozen. Weexplain the crossover scale between the diffusive and subdiffusive transport bybounding the dynamics of the dipole moment for arbitrary initial state. We alsoprove its emergent conservation at infinite temperature. Consequently, thestudied chain is one of the simplest experimentally realizable models for whichnumerical data are consistent with the hydrodynamics of fractons.

Emergent dipole moment conservation and subdiffusion in tilted chains