  We employ a variational Monte Carlo approach to efficiently obtain the
dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the
square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground
state undergoes a continuous transition from a N\'eel antiferromagnet to a
$\mathbb{Z}_{2}$ gapless spin liquid. We identify the characteristic spectral
features in both phases and highlight the existence of a broad continuum of
excitations in the proximity of the spin-liquid phase. The magnon branch, which
dominates the spectrum of the unfrustrated Heisenberg model, gradually loses
its spectral weight, thus releasing nearly-deconfined spinons, whose signatures
are visible even in the magnetically ordered state. Our results show how free
spinons emerge across a quantum critical point, providing evidence for the
fractionalization of magnons into deconfined spinons.
