Exploring limits of dipolar quantum simulators with ultracold molecules

We provide a quantitative blueprint for realizing two-dimensional quantum simulators employing ultracold dipolar molecules or magnetic atoms by studying their accuracy in predicting ground state properties of lattice models with long-range interactions. For experimentally relevant ranges of potential depths, interaction strengths, particle fillings, and geometric configurations, we map out the agreement between the state prepared in the quantum simulator and the target lattice state. We do so by separately calculating numerically exact many-body wave functions in the continuum and single- or multi-band lattice representations, and building their many-body state overlaps. While the agreement between quantum simulator and single-band models is good for deep optical lattices with weaker interactions and low particle densities, the higher band population rapidly increases for shallow lattices, stronger interactions, and in particular above half filling. This induces drastic changes to the properties of the simulated ground state, potentially leading to false predictions. Furthermore, we show that the interplay between commensurability and interactions can lead to quasidegeneracies, rendering a faithful ground state preparation even more challenging.