  Employing large-scale quantum Monte Carlo simulations, we systematically
compute the energy spectra of the 2D spin-1/2 Heisenberg model with long-range
interactions. With the $1/r^{\alpha}$ ferromagnetic and staggered
antiferromagnetic interactions, we find the explicit range in $\alpha$ for
{\color{black} the short-range Goldstone-type (gapless), anomalous
Goldstone-type (gapless) and Higgs-type (gapped) spectra. Accompanied by the
spin wave analysis, our numerical results vividly reveal how the long-range
interactions alter the usual linear and quadratic magnon dispersions in 2D
quantum magnets and give rise to anomalous dynamical exponents. Moreover, we
find explicit case where the gapped excitation exists even when the Hamiltonian
is extensive. This work provides the first set of unbiased dynamical data} of
long-range quantum many-body systems and suggests that many universally
accepted low-energy customs for short-range systems need to be substantially
modified for long-range ones which are of immediate relevance to the ongoing
experimental efforts from quantum simulators to 2D quantum moir\'e materials.
