Fully packed quantum loop model on the square lattice: phase diagram and application for Rydberg atoms

Abstract

The quantum dimer and loop models attract great attentions, partially because the fundamental importance in the phases and phase transitions emerging in these prototypical constrained systems, and partially due to their intimate relevance toward the on-going experiments on Rydberg atom arrays in which the blockade mechanism naturally enforces the local constraint. Here we show, by means of the sweeping cluster quantum Monte Carlo method, the complete ground state phase diagram of the fully packed quantum loop model on the square lattice. We find between the lattice nematic (LN) phase with strong dimer attraction and the staggered phase (SP) with strong dimer repulsion, there emerges a resonating plaquette (RP) phase with off-diagonal translational symmetry breaking. Such a quantum phase is separated from the LN via a first order transition and from the SP by the famous Rokhsar-Kivelson point. Our renormalization group analysis reveals the different flow directions, fully consistent with the order parameter histogram in Monte Carlo simulations. The realization and implication of our phase diagram in Rydberg experiments are proposed.

8 pages, 7 figures

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• Dynamical properties of quantum many-body systems with long range interactions
• Quantum optimization within lattice gauge theory model on a quantum simulator
• Quantum Simulation of Two-Dimensional $\mathrm{U}(1)$ Gauge Theory in Rydberg and Rydberg-Dressed Atom Arrays
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice