Mononpoles and Anomalies of an SU(3) Dirac Spin Liquid on the Kagome Lattice

Quantum spin liquids are a class of exotic phases of interacting spins that host interesting features ranging from long range entanglement to the emergence of gauge theories. We consider a version of an SU(3) Hubbard model on the Kagome lattice. At one-third filling, we obtain a candidate for a Dirac spin liquid (DSL), which does not have a quasi-particle description. We show how aspects of the band topology and crystalline symmetries can constrain the stability properties of the DSL through determining the quantum numbers of the monopole operators. This extends methods previously applied for SU(2) and SU(4) spin systems. Further, we calculate the quantum anomalies of the low energy quantum field theory and comment on the possible phases this system can realize.