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Quantum loop and dimer models are archetypal examples of correlated systemswith local constraints, whose generic solutions are difficult to obtain due tothe lack of controlled methods to solve them in the thermodynamic limit. Yet,these solutions are of immediate relevance towards both statistical and quantumfield theories, as well as the fast-growing experiments in Rydberg atom arraysand quantum moir\'e materials, where the interplay between correlation andlocal constraints gives rise to a plethora of novel phenomena. In a recentwork[1], it was found via sweeping cluster quantum Monte Carlo (QMC)simulations and field theory analysis that the triangular lattice quantum loopmodel (QLM) hosts a rich ground state phase diagram with lattice nematic (LN),vison plaquette (VP) crystals, and the $\mathbb{Z}_2$ quantum spin liquid (QSL)close to the Rokhsar-Kivelson (RK) point. Here, we focus on the continuousquantum critical point separating the VP and QSL phases and demonstrate viaboth static and dynamic probes in QMC simulations that this transition is ofthe (2+1)d Cubic* universality, in which the fractionalized visons in QSLcondense to give rise to the crystalline VP phase, while leaving their trace inthe anomalously large anomalous dimension exponent and pronounced continua inthe dimer and vison spectra compared with those at the conventional Cubic orO(3) quantum critical points.

Cubic* criticality emerging from quantum loop model on triangular lattice