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

Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons