Quantum simulation of the fermionic Hubbard model

Strongly correlated quantum materials, such as high-temperature superconductors, hold great promise for driving future technological advances. However, their underlying physical mechanisms remain unclear, posing significant challenges for scalable and controlled preparation and application. The fermionic Hubbard model (FHM), which describes electron motion in a lattice, is considered one of the key models for understanding high-temperature superconductors. Yet, resolving its low-temperature phase diagram remains difficult, both theoretically and numerically. Ultracold Fermi atoms in optical lattices provide a clean and highly controllable platform for simulating the FHM. In this talk, I will present our recent progress in quantum simulations of the FHM. We have constructed a homogeneous fermionic Hubbard system with approximately 800,000 lattice sites at temperatures below the Néel temperature. Using radio-frequency spectroscopy, we precisely measured the double occupancy fraction, revealing the Pomeranchuk effect. Additionally, we employed spin-sensitive Bragg scattering techniques to measure the spin structure factor of the system. When interaction strength, temperature, and doping concentration are finely tuned to their respective critical values, we observed a sharp increase in the spin structure factor. These observations can be well described by a power-law divergence, providing conclusive evidence for the realization of the antiferromagnetic phase transition.