We perform an exact-diagonalization study of the spin-$\frac{1}{2}$ XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization $m=\frac{2}{3}$ with an emphasis on the $XY$ point $\left(J_z=0\right)$ and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014)] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of ${\sigma }_{xy}=\frac{1}{2}$. Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the ${\sigma }_{xy}=\frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

• Received 22 June 2016
• Revised 21 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.134410