Nature of spin-liquid phase in 2D spin-1/2 J_1-J_2 triangular antiferromagnet

We study the stability of ordered states in a two-dimensional quantum spin-1/2 J_1-J_2 XY antiferromagnet on a frustrated triangular lattice using composite fermion representation of spins. In the presence of next-nearest-neighbor antiferromagnetic coupling, J_2, the model is shown to undergo a continuous transition from $120^\circ$ ordered state to a quantum U(1) Dirac spin-liquid (QED_3) at J_2/J_1 ~ 0.089, in accordance with previous variational Monte-Carlo and DMRG studies. In the XY limit, the U(1) gauge field emerges in a narrow parameter interval of 0.089\lesssim J_2/J_1 \lesssim 0.116, that stabilizes the spin liquid. The transition to the tripe phase at J_2/J_1 \sim 0.116 is found to be of first order. Finite Ising interaction, J_z, pushes the boundaries of the phase transitions to $120^\circ$ state and the stripe ordered state apart, thus opening a wider interval for the spin-liquid. Our results show an interesting interplay of ordering and the emergence of the gauge field in the vicinity of unconventional criticality.