Detail:
Abstract: We have performed large scale variational search for the best RVB ansatz for the spin-12 kagome antiferromagnet with both nearest-neighboring(NN) and next-nearest-neighboring(NNN) exchanges assuming only translational symmetry. We find the best RVB state is always fully symmetric and has an mean field ansatz that is gauge equivalent to a previous proposed Z2 spin liquid ansatz. The Z2 state is found to be slightly more stable than the extensively studied U(1) gapless Dirac spin liquid state in both the J2≠0 and the J2=0 case and to possess a small spinon gap for J2<0 .2. the breaking of the u(1) gauge symmetry in the z2 state is found to increase with j2 and to be quite substantial around j2="0.15." however, we find the z2 state is always very close to the gapless u(1) dirac spin liquid state, although they have very different rvb parameters. we argue the kagome antiferromagnet should be better understood as a near critical system, rather than a system deep inside a gapped spin liquid phase with well established z2 topological order.
