Tripartite entangled plaquette state in a cluster magnet

Using large-scale quantum Monte Carlo simulations we show that a spin-$\frac{1}{2}\phantom{\rule{1em}{0ex}}XXZ$ 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 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 trimerized optical kagome lattices.