Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

Abstract: By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-$1/2$ Heisenberg model with the first-neighbor ($J_1$), second-neighbor ($J_2$), and additional scalar chiral interaction $J_{\chi}{\bf S}i \cdot ({\bf S}_j \times {\bf S}_k)$ on the triangular lattice. In the non-magnetic phase of the $J_1-J_2$ triangular model with $0.08 \lesssim J_2/J_1 \lesssim 0.16$, recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B {\bf 92}, 041105 (2015); Hu, Gong, Zhu, and Sheng, Phys. Rev. B {\bf 92}, 140403 (2015)] find a possible gapped spin liquid with the signal of a competition between a chiral and a $Z_2$ spin liquid. Motivated by the DMRG results, we consider the chiral interaction $J{\chi}{\bf S}i \cdot ({\bf S}_j \times {\bf S}_k)$ as a pertubation for this non-magnetic phase. We find that with growing $J{\chi}$, the gapless U(1) Dirac spin liquid, which has the best variational energy for $J_{\chi}=0$, exhibits the energy instability towards a gapped spin liquid with non-trivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number $C=1/2$ and two-fold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the non-magnetic phase of the $J_1-J_2$ triangular model.