Antiferromagnetic phase transition in a 3D fermionic Hubbard model

Hou-Ji Shao, Yu-Xuan Wang, Zhu De-Zhi, Yan-Song Zhu, Hao-Nan Sun, Si-Yuan Chen, Chi Zhang, Zhi-Jie Fan, Youjin Deng, Xing-Can Yao (), Yu-Ao Chen () and Jian-Wei Pan ()
Additional contact information
Hou-Ji Shao: University of Science and Technology of China
Yu-Xuan Wang: University of Science and Technology of China
Zhu De-Zhi: University of Science and Technology of China
Yan-Song Zhu: University of Science and Technology of China
Hao-Nan Sun: University of Science and Technology of China
Si-Yuan Chen: University of Science and Technology of China
Chi Zhang: University of Science and Technology of China
Zhi-Jie Fan: University of Science and Technology of China
Youjin Deng: University of Science and Technology of China
Xing-Can Yao: University of Science and Technology of China
Yu-Ao Chen: University of Science and Technology of China
Jian-Wei Pan: University of Science and Technology of China

Nature, 2024, vol. 632, issue 8024, 267-272

Abstract: Abstract The fermionic Hubbard model (FHM)1 describes a wide range of physical phenomena resulting from strong electron–electron correlations, including conjectured mechanisms for unconventional superconductivity. Resolving its low-temperature physics is, however, challenging theoretically or numerically. Ultracold fermions in optical lattices2,3 provide a clean and well-controlled platform offering a path to simulate the FHM. Doping the antiferromagnetic ground state of a FHM simulator at half-filling is expected to yield various exotic phases, including stripe order4, pseudogap5, and d-wave superfluid6, offering valuable insights into high-temperature superconductivity7–9. Although the observation of antiferromagnetic correlations over short10 and extended distances11 has been obtained, the antiferromagnetic phase has yet to be realized as it requires sufficiently low temperatures in a large and uniform quantum simulator. Here we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature and doping concentration are finely tuned to approach their respective critical values, a sharp increase in the spin structure factor is observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class12. At half-filling and with optimal interaction strength, the measured spin structure factor reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results provide opportunities for exploring the low-temperature phase diagram of the FHM.

Date: 2024
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DOI: 10.1038/s41586-024-07689-2

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