Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m=2/3 magnetization

We perform an exact-diagonalization study of the spin-1/2 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m = 2/3 with an emphasis on the XY point (J(z) = 0) 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) = 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) = 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.