Global phase diagram and quantum spin liquids in a spin- 12 triangular antiferromagnet

We study the spin-1/2 Heisenberg model on the triangular lattice with the nearest-neighbor J1>0, the next-nearest-neighobr J2>0 Heisenberg interactions, and the additional scalar chiral interaction Jχ(Si×Sj)·Sk for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing J2 (J2/J1≤0.3) and Jχ (Jχ/J1≤1.0) interactions, we establish a quantum phase diagram with the magnetically ordered 120°, stripe, and noncoplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a ν=1/2 bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the J1-J2 triangular model (0.08J2/J10.15) shows a phase transition to the CSL phase at very small Jχ. We also compute the spin triplet gap in both spin liquid phases, and our finite-size results suggest a large gap in the odd topological sector but a small or vanishing gap in the even sector. We discuss the implications of our results on the nature of the spin liquid phases.