Simulation of gauge transformations on systems of ultracold atoms

In this paper, we propose a method for simulating gauge transformations on ultracold atoms trapped in an optical lattice coupled to an artificial magnetic field. We discuss an observable that is invariant under these gauge transformations and compute it using a tensor network ansatz that escapes the phase problem. We find 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 entanglement in the variational ansatz.