Kinetic magnetism and stripe order in the antiferromagnetic bosonic ${t-J}$ model

Unraveling the microscopic mechanisms governing the physics of doped quantum magnets is key to advancing our understanding of strongly correlated quantum matter. Quantum simulation platforms, e.g., ultracold atoms in optical lattices or tweezer arrays, provide a powerful tool to investigate the interplay between spin and charge motion in microscopic detail. Here, in a new twist, we disentangle the role of particle statistics from the physics of strong correlations by exploring the strong coupling limit of doped \emph{bosonic} quantum magnets, specifically the antiferromagnetic (AFM) bosonic $t-J$ model. Using large-scale density matrix renormalization group (DMRG) calculations, we map out the phase diagram on the 2D square lattice at finite doping. In the low-doping regime, bosonic holes form partially-filled stripes, akin to those observed in high-$T_c$ cuprates. As doping increases, a transition occurs to a partially-polarized ferromagnetic (FM) phase, driven by the motion of mobile bosonic charge carriers forming Nagaoka polarons. At high doping or large $t/J$, the system evolves into a fully-polarized ferromagnet. These findings shed new light on the role of particle statistics in strongly correlated many-body systems, revealing connections to stripe formation and the physics of kinetic (i.e., Nagaoka-type) ferromagnetism. Our results may be realized in state-of-the-art quantum simulation platforms with bosonic quantum gas microscopes and Rydberg atom tweezer arrays, paving the way for future experimental studies of doped bosonic quantum magnets.