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

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 off-diagonal 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.

The frustration-free fully packed loop model

“…the ergodicity breaking for FPL models adopted to non-bipartite lattices. Lattices of interest include the triangular one [70][71][72], or more exotic ones such as the Kagome lattice [73], or even aperiodic tilings like the Penrose [74] and the Amman-Beenker tiling.…”

Hilbert space fragmentation in a frustration-free fully packed loop model

“…One may also expect the emergence of interesting phases and refined structures in the Hilbert space fragmentation for fully packed loop models adopted to nonbipartite lattices. Lattices of interest include the triangular one [65][66][67], or more exotic ones such as the Kagome lattice [68], or even aperiodic tilings like the Penrose [69] and the Amman-Beenker tiling.…”

Preparing state within target topological sector of lattice gauge theory model on quantum simulator

“…One of the most interesting directions in quantum simulation is to construct lattice gauge theory (LGT) Hamiltonian and its nontrivial quantum states via Rydberg arrays, superconducting circuits and other platforms [1,2,6,7]. Quantum dimer model as a typical LGT is widely prepared in certain highly frustrated parameter region of Rydberg arrays [8][9][10][11][12][13]. L-GT models have Hilbert space fragmentation due to local constraints, the sub-Hilbert spaces are labelled by different winding numbers and protected by topological defects.…”