Antiferromagnetic phase transition in a 3D fermionic Hubbard model

Hou-Ji Shao; Yu-Xuan Wang; De-Zhi Zhu; Yan-Song Zhu; Hao-Nan Sun; Si-Yuan Chen; Chi Zhang; Zhi-Jie Fan; Youjin Deng; Xing-Can Yao; Yu-Ao Chen; Jian-Wei Pan

doi:10.1038/s41586-024-07689-2

Antiferromagnetic phase transition in a 3D fermionic Hubbard model

Nature. 2024 Aug;632(8024):267-272. doi: 10.1038/s41586-024-07689-2. Epub 2024 Jul 10.

Authors

Hou-Ji Shao^#^{1

2}, Yu-Xuan Wang^#^{1

2}, De-Zhi Zhu^{1

2}, Yan-Song Zhu^{1

2}, Hao-Nan Sun^{1

2}, Si-Yuan Chen^{1

2}, Chi Zhang^{1

2}, Zhi-Jie Fan^{1

2

3}, Youjin Deng^{1

2

3}, Xing-Can Yao^{4

5

6}, Yu-Ao Chen^{7

8

9}, Jian-Wei Pan^{10

11

12}

Affiliations

¹ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
² Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China.
³ Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
⁴ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China. yaoxing@ustc.edu.cn.
⁵ Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China. yaoxing@ustc.edu.cn.
⁶ Hefei National Laboratory, University of Science and Technology of China, Hefei, China. yaoxing@ustc.edu.cn.
⁷ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China. yuaochen@ustc.edu.cn.
⁸ Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China. yuaochen@ustc.edu.cn.
⁹ Hefei National Laboratory, University of Science and Technology of China, Hefei, China. yuaochen@ustc.edu.cn.
¹⁰ Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China. pan@ustc.edu.cn.
¹¹ Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China. pan@ustc.edu.cn.
¹² Hefei National Laboratory, University of Science and Technology of China, Hefei, China. pan@ustc.edu.cn.

^# Contributed equally.

PMID: 38987606
DOI: 10.1038/s41586-024-07689-2

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 lattices^2,3 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 superconductivity^7-9. 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.