Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a suitable 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 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 Z₂ 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.

在承载任意子激发和拓扑阶数的量子多体模型中，量子二聚体模型（QDM）提供了一个合适的场所，用于研究单子午和多子午连续谱之间的关系。但是，作为具有局部约束的原型相关系统，由于缺少受控方法，因此在不同晶格几何形状和参数范围内的QDM通用解决方案仍然缺失。在这里，我们通过扫描簇量子蒙特卡罗算法获得了三角晶格QDM不同相位的激发光谱。我们的结果揭示了Z ₂量子自旋液体（QSL）内部的单光子激发及其向\（\ sqrt {12} \ times \ sqrt {12} \）的凝结价键固体（VBS），并证明了QSL-VBS过渡处的平移对称性分级和新兴O（4）对称性。我们发现单维森激发，其卷积定性地再现了二聚体光谱，不是自由的，而是在整个过渡过程中都受到相互作用的影响。全面揭示了VBS及其O（4）顺序参数的性质。我们的方法为QDM静态和动态属性的通用解决方案开辟了道路，并且与可编程量子模拟器中分数激发的实现和检测相关。