# Tripartite entangled plaquette state in a cluster magnet

## TL;DR

This paper uses quantum Monte Carlo simulations to identify a tripartite entangled plaquette state in a 2D anisotropic Kagome lattice spin model, revealing its phase transitions and potential relevance to quantum materials and optical lattice systems.

## Contribution

It demonstrates the existence of a tripartite entangled plaquette state in a Kagome lattice XXZ model and explores its phase diagram and transitions, connecting to experimental systems.

## Key findings

- Identified a tripartite entangled plaquette state preserving all Hamiltonian symmetries.
- Mapped out the phase diagram and phase transitions involving this state.
- Connected the findings to charge dynamics in a Hubbard model and optical lattice realizations.

## Abstract

Using large-scale quantum Monte Carlo simulations we show that a spin-$1/2$ XXZ model on a two-dimensional anisotropic Kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break U(1) and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the description of the spin liquid candidate ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, as well as a model of strongly correlated bosonic atoms loaded onto highly tunable {\it trimerized} optical Kagome lattices.