Symmetry-broken phases proximate to Z2 spin liquid on Kagome lattice

Recently, $Z_{2}$ spin liquid was proposed as the ground state of the Kagome quantum antiferromagnet [S. Yan, D.A. Huse, and S.R. White, {\it Science}, 332, 1173 (2011)]. We study proximate symmetry-broken phases that may appear on exiting the spin liquid phase, by tuning parameters such as further neighbor couplings. Given that the Dirac spin liquid is also a relatively low energy state, we consider models of $Z_{2}$ spin liquids that are proximate to it. Specifically we consider the s-wave paired state of an algebraic spin liquid on Kagome lattice, $Z_{2} [0,\pi]\beta$ state of Y.-M Lu, Y. Ran, and P.A. Lee, {\it Phys. Rev.} B 83, 224413 (2011)] and examine its relations with other competing states. This allows us to characterize the proximate magnetically ordered and VBS phases and criticality between them and the quantum spin liquid.