Metastable ferromagnetic clusters in dissipative many-body systems of polar molecules

We investigate the effect of two-body loss due to chemical reactions on quantum magnetism of fermionic polar molecules in an optical lattice. We show that an interplay between dissipation and strong long-range interactions leads to formation of metastable ferromagnetic clusters. The spin states of clusters are controlled by interaction parameters and reflect the symmetry of interactions. The size of clusters strongly depends on the initial configuration of molecules due to Hilbert-space fragmentation during dissipative many-body dynamics. We construct an effective model to show the emergence of metastable states as quasi-dark states. Application to quantum simulation of the spin-$S$ Heisenberg model is discussed.