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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 α ferromagnetic and staggered antiferromagnetic interactions, we find the explicit range in α for the Goldstone-type (gapless) and Higgs-type (gapped) spectra. Accompanied by the spin wave analysis, our results vividly reveal how the long-range interactions induce a mass to the Goldstone mode via the generalized Higgs mechanism. This work provides the first set of unbiased dynamical properties 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 moiré materials.

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