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We propose an experimentally feasible setup with ultracold alkaline earthatoms to simulate the dynamics of U(1) lattice gauge theories in 2+1 dimensionswith a Chern-Simons term. To this end we consider the ground state propertiesof spin-5/2 alkaline earth fermions in a honeycomb lattice. We use theGutzwiller projected variational approach in the strongly repulsive regime inthe case of filling 1/6. The ground state of the system is a chiral spin liquidstate with $2\pi/3$ flux per plaquette, which spontaneously violates timereversal invariance. We demonstrate that due to the breaking of time reversalsymmetry the system exhibits quantum Hall effect and chiral edge states. Werelate the experimentally accessible spin fluctuations to the emerging gaugefield dynamics. We discuss also properties of the lowest energy competingorders.

Gauge fields emerging from time reversal symmetry breaking for spin-5/2 fermions in a honeycomb lattice