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We show that the best variational ground state of the spin-$\frac{1}{2}$Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchangecoupling(NN-KAFH) is a $Z_{2}$ spin liquid state, rather than the widelybelieved $U(1)$ Dirac spin liquid state. The spinon excitation in the $Z_{2}$spin liquid state has a small gap of about $1/40$ of the spinon band width. Wefind that while the $Z_{2}$ and the $U(1)$ spin liquid state have a largeoverlap on finite clusters and are thus very close in energy, they host totallydifferent spinon excitation spectrum. The strength of the RVB theory becomesparticularly clear in such a situation, as it provides not only a variationalunderstanding of the ground state structure, but also a comprehensive picturefor the excitation spectrum of the system. Our result indicates that thespin-$\frac{1}{2}$ NN-KAFH should be better understood as a nearly criticalsystem, rather than a prototypical gapped $Z_{2}$ spin liquid system.

$Z_{2}$ spin liquid ground state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model