Lattice control of non-ergodicity in a polar lattice gas

Inter-site interactions in polar lattice gases may result, due to Hilbert-space fragmentation, in a lack of ergodicity even in absence of disorder. We show that the inter-site interaction in a one-dimensional dipolar gas in an optical lattice departs from the usually considered $1/r^3$ dependence, acquiring a universal form that depends on the transversal confinement and the lattice depth. Due to the crucial role played by the nearest- and next-to-nearest neighbors, the Hilbert-space fragmentation and particle dynamics are very similar to that of a power-law model $1/r^{\beta_{\mathrm{eff}}<3}$, where $\beta_{\mathrm{eff}}$ is experimentally controllable by properly tailoring the transversal confinement. Our results are of direct experimental relevance for experiments on dipolar gases in optical lattices, and show that the particle dynamics may be remarkably different if the quasi-1D lattice model is realized in a strong 3D lattice, or by means of a strong transversal harmonic confinement.