Quantifying the impact of dipolar interactions on the accuracy of ultracold quantum simulators and the stability of their many-body phases

Rapid experimental advances in controlling ultracold magnetic atoms and dipolar molecules are making it possible to realize and study enticing quantum states of matter that encapsulate novel properties conferred by long-range interactions. This progress, however, comes with several caveats. A first, more fundamental question is how long-range interactions impact the physics of paradigmatic models that have been studied with short-range interactions thus far. Another, more technical question revolves around how accurately such models can actually be realized in experiments. In this talk, I will present recent results that address both questions. First, I will show how dipolar interactions can strongly enrich many-body phases of matter and their thermodynamic properties with examples from interacting quasicrystals and super-Tonks-Girardeau states. In these systems, dipolar interactions can either strengthen or weaken localization and prethermalization phenomena depending on their magnitude, even leading to new phases. I will then provide a quantitative blueprint for the realization of near-term dipolar quantum simulators in one and two dimensions by systematically comparing their physics to that of the lattice models they purportedly quantum simulate. I will demonstrate that in regimes of high filling and high interactions, strong quantitative discrepancies inevitably arise. This is due to higher band occupation caused by the long-range nature of dipolar interactions, and can have striking consequences for the correct prediction of ground-state properties.