  Deconfined quantum critical points govern continuous quantum phase
transitions at which fractionalized (deconfined) degrees of freedom emerge.
Here we study dynamical signatures of the fractionalized excitations in a
quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum
critical point with emergent O(4) symmetry. By means of large-scale quantum
Monte Carlo simulations and stochastic analytic continuation of imaginary-time
correlation functions, we obtain the dynamic spin structure factors in the
$S^{x}$ and $S^{z}$ channels. In both channels, we observe broad continua that
originate from the deconfined excitations. We further identify several distinct
spectral features of the deconfined quantum critical point, including the lower
edge of the continuum and its form factor on moving through the Brillouin Zone.
We provide field-theoretical and lattice model calculations that explain the
overall shapes of the computed spectra, which highlight the importance of
interactions and gauge fluctuations to explaining the spectral-weight
distribution. We make further comparisons with the conventional Landau O(2)
transition in a different quantum magnet, at which no signatures of
fractionalization are observed. The distinctive spectral signatures of the
deconfined quantum critical point suggest the feasibility of its experimental
detection in neutron scattering and nuclear magnetic resonance experiments.
