Spin-1/2 Heisenberg J1-J2 antiferromagnet on the kagome lattice

We report variational Monte Carlo calculations for the spin-1/2 Heisenberg model on the kagome lattice in the presence of both nearest-neighbor J(1) and next-nearest-neighbor J(2) antiferromagnetic superexchange couplings. Our approach is based upon Gutzwiller projected fermionic states that represent a flexible tool to describe quantum spin liquids with different properties (e.g., gapless and gapped). We show that, on finite clusters, a gapped Z(2) spin liquid can be stabilized in the presence of a finite J(2) superexchange, with a substantial energy gain with respect to the gapless U(1) Dirac spin liquid. However, this energy gain vanishes in the thermodynamic limit, implying that, at least within this approach, the U(1) Dirac spin liquid remains stable in a relatively large region of the phase diagram. For J(2)/J(1) greater than or similar to 0.3, we find that a magnetically ordered state with q = 0 overcomes the magnetically disordered wave functions, suggesting the end of the putative gapless spin-liquid phase.