Kinetic Magnetism in a Bosonic t–J Model: From Antiferromagnetism to Nagaoka Ferromagnetism

High-temperature superconductivity is widely believed to emerge from the competition between kinetic and magnetic processes, effectively captured by Hubbard or t–J models with antiferromagnetic exchange couplings. At low doping levels, magnetic correlations dominate, stabilizing antiferromagnetic order, whereas at high doping kinetic motion prevails, yielding a conventional Fermi liquid. Here we explore a bosonic variant of the t–J model with antiferromagnetic exchange interactions, realized using dopants obeying bosonic statistics. Such systems are now experimentally accessible, as demonstrated in Rydberg tweezer arrays [Qiao et al., Nature 644, 889–895 (2025)] and in bosonic quantum gas microscopes operating at negative absolute temperatures [Bohrdt et al., arXiv:2410.19500]. Using large-scale density-matrix renormalization group (DMRG) simulations, we uncover a rich phase diagram where the interplay between kinetic and magnetic effects drives a transition from antiferromagnetism at low doping to an extended kinetic ferromagnet at high doping, continuously connected to the Nagaoka ferromagnet in the limit of vanishing exchange interactions. At intermediate dopings, we find signatures of ferromagnetic bubble polarons—localized holes binding to finite magnetization clouds within an antiferromagnetic background. This regime is directly observable in quantum gas microscopes. At lower dopings, we identify partially filled stripe states, reminiscent of those in the fermionic t–J model, supporting the notion that stripes act as quasi-one-dimensional channels where the dopant statistics can be effectively transformed via a Jordan–Wigner mapping constrained to the stripe. As an outlook, we discuss the possibility of bound states constituted by overlapping bubble polarons, which may provide new routes toward unconventional pairing mechanisms.