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

TL;DR

This paper maps the complete phase diagram of a fully packed quantum loop model on a square lattice using quantum Monte Carlo, revealing a resonating plaquette phase relevant for Rydberg atom experiments.

Contribution

It provides the first comprehensive ground state phase diagram of the fully packed quantum loop model on the square lattice, including the discovery of a resonating plaquette phase.

Findings

Identification of a resonating plaquette phase with translational symmetry breaking

First order transition between lattice nematic and resonating plaquette phases

Location of the Rokhsar-Kivelson point separating phases

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.