Antiferromagnetic Bosonic t–J Models and Their Quantum Simulation in Tweezer Arrays

The combination of optical tweezer arrays with strong interactions---via dipole exchange of molecules and Van der Waals interactions of Rydberg atoms---has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants. This will enable one to simulate the physics believed to underlie many strongly correlated quantum materials. Here, we propose an experimental scheme to realize bosonic t--J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-T₂ cuprates can be realized. Since the ground states of the 2D bosonic AFM t--J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants---the simplest instance in which their bosonic statistics plays a role---and compare our results to the fermionic case. We perform large-scale density matrix renormalization group calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t--J models may contain similar physics as the collective phases in strongly correlated electrons.