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Quantum loop and dimer models are prototypical correlated systems with localconstraints, whose generic solutions for different lattice geometries andparameter regimes are still missing due to the lack of controlled methods tosolve such systems in the thermodynamic limit. Here, we obtain, via the newlydeveloped sweeping cluster quantum Monte Carlo algorithm, the phase diagram ofthe triangular-lattice fully packed quantum loop model (quantum dimer modelwith two dimers per site). We find that as the interaction turns fromattractive to repulsive, the system has a first-order transition from a latticenematic (LN) solid to a novel vison plaquette (VP) solid without dimer densitymodulations but with off-diagonal order. Further increasing the dimer repulsiontowards the Rokhsar-Kivelson point, the VP phase experiences a continuoustransition to an even $\mathbb{Z}_2$ quantum spin liquid (QSL) phase. Ourresults reveal the LN-to-VP first-order transition is triggered by theintricate change from face- to corner-cubic anisotropy of the O($3$) visonorder parameter, and the VP-to-QSL continuous transition is of the cubicuniversality class, which is very close to the $(2+1)$D O($3$) one, in fullconsistency with the recent conformal bootstrap findings on the cubic fixedpoint.

Fully packed quantum loop model on the triangular lattice: Hidden vison plaquette phase and cubic phase transitions