  We show that gauge transformations can be simulated on systems of ultracold
atoms. We discuss observables that are invariant under these gauge
transformations and compute them using a tensor network ansatz that escapes the
phase problem. We determine that the Mott-insulator-to-superfluid critical
point is monotonically shifted as the induced magnetic flux increases. This
result is stable against the inclusion of a small amount of entanglement in the
variational ansatz.
