Chiral spin liquid phase in an optical lattice at mean-field level

We study an optical Raman square lattice with U(1) synthetic gauge flux to show a chiral spin liquid (CSL) phase for cold atoms based on slave-rotor and spinon mean-field theories, respectively. An effective U(1) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find the CSL phase at a strong on-site Fermi Hubbard interacting regime. For large value of Hubbard interaction, we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that the CSL phase is stabilized in the case of strong magnetic frustration. Two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.