Phase diagram of an easy-axis Kagome antiferromagnet under a magnetic field

We present a quantum Monte-Carlo (QMC) study of a spin-1/2 XXZ model, with second and third-neighbour terms, under a magnetic field on the Kagome lattice. This model, introduced in the zero field case by Balents, Fisher and Girvin [1], exhibits, in the easy-axis limit, a topological gapped Z2 phase with fractional excitation [2-4]. When adding a magnetic field, other gapped incompressible phases are stable for magnetizations 1/3 and 2/3 of its saturation value. Using state-of-the-art measurements, including recently developped tools to compute the topological entropy, we investigate the nature of these ground-states. Finally, we make some connection between these microscopic models and effective constrained models (such as quantum loop model or quantum dimer model respectively), which allow to provide a better understanding of the physical properties. \\[4pt] [1] L. Balents, M. P. A. Fisher, and S. M. Girvin, Phys. Rev. B {\bf 65}, 224412 \\[0pt] [2] S. V. Isakov, Y. B. Kim, and A. Paramekanti, Phys. Rev. Lett. {\bf 97}, 207204 (2006) \\[0pt] [3] S. V. Isakov, M. B. Hastings, and R. G. Melko, Nat. Phys. {\bf 7}, 772 (2011) \\[0pt] [4] S. V. Isakov, R. G. Melko, and M. B. Hastings, Science {\bf 335}, 193 (2012)