Chiral And Critical Spin Liquids In A Spin- 1/2 Kagome Antiferromagnet

The kagome spin-12 systems have attracted intensive attention in recent years as the primary candidate for hosting different gapped spin liquids (SLs). To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest-neighbor (NN) (Jxy), the second-NN, and the third-NN couplings (J2xy=J3xy=J′xy). We identify the time-reversal-symmetry-broken chiral SL (CSL) with the turn on of a small perturbation J′xy∼0.06Jxy, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the ν=1/2 fractional quantum Hall state. Interestingly, the NN XY model (J′xy=0) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet and spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. The effect of the NN spin-z coupling Jz is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL.