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**Michael L. Wall and Lincoln D. Carr**

**Department of Physics, Colorado School of Mines**

**We study the effective dipole-dipole interactions in an ultracold quantum gas loaded into an optical lattice. As opposed to the 1/r^3 decay of interactions between dipoles separated by a distance r in free space, we find that the effective interaction in the lattice decays exponentially with separation at short distance and has a long-range power law tail. The increased effective interaction is due to large quantum fluctuations from the heavy-tailed localized single-particle probability distributions, and also relies crucially on imbalance in confinement due to the d-wave anisotropy of the dipole-dipole interaction. The effect can be sizable in quasi-low dimensional confined scenarios; we identify differences of up to 36% from the free-space interaction at the nearest-neighbor distance in quasi-1D arrangements. Using matrix product state simulations on infinite quasi-one-dimensional lattices, we demonstrate that use of the correct lattice dipolar interaction leads to significant deviations from many-body predictions using the free-space interaction in the lattice.**

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