Chern-Simons fermionization approach to the chiral spin liquid on a frustrated square lattice with moat band

We utilize the Chern-Simons (CS) fermionization to study quantum spin XY models on a square lattice in the regime where the lattice dispersion exhibits a moat-like structure. We analytically derive the low-energy effective field theory, and predict a possible non-uniform chiral spin-liquid (CSL) ground state. Using high-precision numerical calculations such as the tensor network renormalization group based on projected entangled paired state (PEPS), we obtain numerical evidences that further suggest the stabilization of the non-uniform CSL. Finally, we show that the CS fermionization approach is also able to describe the magnetically ordered phases, which are captured by a CS superconducting state with condensation of Cooper pairs of CS fermions. By comparing the Goldstone mode of the magnetically ordered phase and that of the CS superconductor, we found high-precision agreements that suggest the equivalence of the two states in terms of the low-energy excitations.