Abstract
Quantum loop and dimer models are prototypical correlated systems with local constraints, whose generic solutions for different lattice geometries and parameter regimes are still missing due to the lack of controlled methods to solve such systems in the thermodynamic limit. Here, we obtain, via the newly developed sweeping cluster quantum Monte Carlo algorithm, the phase diagram of the triangular-lattice fully packed quantum loop model (quantum dimer model with two dimers per site). We find that as the interaction turns from attractive to repulsive, the system has a first-order transition from a lattice nematic (LN) solid to a novel vison plaquette (VP) solid without dimer density modulations but with kinetic-term order. Further increasing the dimer repulsion towards the Rokhsar-Kivelson point, the VP phase experiences a continuous transition to an even Z2 quantum spin liquid (QSL) phase. Our results reveal the LN-to-VP first-order transition is triggered by the intricate change from face- to corner-cubic anisotropy of the O(3) vison order parameter, and the VP-to-QSL continuous transition is of the cubic universality class, which is very close to the (2+1)D O(3) one, in full consistency with the recent conformal bootstrap findings on the cubic fixed point.
Reference:
Zheng Yan#, Xiaoxue Ran#, Yan-Cheng Wang, Rhine Samajdar, Junchen Rong, Subir Sachdev, Yang Qi*, Zi Yang Meng*, arXiv:2205.04472 (2022)
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