  Based on the mapping between $s=1/2$ spin operators and hard-core bosons, we
extend the cluster perturbation theory to spin systems and study the whole
excitation spectrum of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model
on the square lattice. In the N\'eel phase for $J_{2}\lesssim0.4J_{1}$, in
addition to the dominant magnon excitation, there is an obvious continuum close
to $(\pi,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon
excitations. In the stripe phase for $J_{2}\gtrsim0.6J_{1}$, we find similar
high-energy two-spinon continuums at $(\pi/2,\pi/2)$ and $(\pi/2,\pi)$,
respectively. The intermediate phase is characterized by a spectrum with
completely deconfined broad continuum, which is attributed to a $Z_{2}$ quantum
spin liquid with the aid of a variational-Monte-Carlo analysis.
