  Among the quantum many-body models that host anyon excitation and topological
orders, quantum dimer models (QDM) provide a unique playground for studying the
relation between single-anyon and multi-anyon continuum spectra. However, as
the prototypical correlated system with local constraints, the generic solution
of QDM at different lattice geometry and parameter regimes is still missing due
to the lack of controlled methodologies. Here we obtain, via the newly
developed sweeping cluster quantum Monte Carlo algorithm, the excitation
spectra in different phases of the triangular lattice QDM. Our results reveal
the single vison excitations inside the $Z_2$ quantum spin liquid (QSL) and its
condensation towards the $\sqrt{12}\times\sqrt{12}$ valence bond solid (VBS),
and demonstrate the translational symmetry fractionalization and emergent O(4)
symmetry at the QSL-VBS transition. We find the single vison excitations, whose
convolution qualitatively reproduces the dimer spectra, are not free but
subject to interaction effects throughout the transition. The nature of the VBS
with its O(4) order parameters are unearthed in full scope. Our approach opens
the avenue for generic solution of the static and dynamic properties of QDMs
and has relevance towards the realization and detection of fractional
excitations in programmable quantum simulators.
