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Shao HJ, Wang YX, Zhu DZ, Zhu YS, Sun HN, Chen SY, Zhang C, Fan ZJ, Deng Y, Yao XC, Chen YA, Pan JW. Antiferromagnetic phase transition in a 3D fermionic Hubbard model. Nature 2024; 632:267-272. [PMID: 38987606 DOI: 10.1038/s41586-024-07689-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 06/07/2024] [Indexed: 07/12/2024]
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.
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Affiliation(s)
- Hou-Ji Shao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - Yu-Xuan Wang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - De-Zhi Zhu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - Yan-Song Zhu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - Hao-Nan Sun
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - Si-Yuan Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - Chi Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
| | - Zhi-Jie Fan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China
| | - Youjin Deng
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- 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
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China
| | - Xing-Can Yao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
- 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.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
| | - Yu-Ao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
- 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.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
- 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.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
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Wang L, Yan X, Min J, Sun D, Xie X, Peng SG, Zhan M, Jiang K. Scale Invariance of a Spherical Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2024; 132:243403. [PMID: 38949354 DOI: 10.1103/physrevlett.132.243403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 04/06/2024] [Accepted: 05/21/2024] [Indexed: 07/02/2024]
Abstract
A unitary Fermi gas in an isotropic harmonic trap is predicted to show scale and conformal symmetry that have important consequences in its thermodynamic and dynamical properties. By experimentally realizing a unitary Fermi gas in an isotropic harmonic trap, we demonstrate its universal expansion dynamics along each direction and at different temperatures. We show that as a consequence of SO(2,1) symmetry, the measured release energy is equal to that of the trapping energy. We further observe the breathing mode with an oscillation frequency twice the trapping frequency and a small damping rate, providing the evidence of SO(2,1) symmetry. In addition, away from resonance when scale invariance is broken, we determine the effective exponent γ that relates the chemical potential and average density along the BEC-BCS crossover, which qualitatively agrees with the mean field predictions. This Letter opens the possibility of studying nonequilibrium dynamics in a conformal invariant system in the future.
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Affiliation(s)
| | - Xiangchuan Yan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | | | - Dali Sun
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | | | - Shi-Guo Peng
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Mingsheng Zhan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Kaijun Jiang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
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Cuestas E, Majtey AP. A generalized molecule approach capturing the Feshbach-induced pairing physics in the BEC-BCS crossover. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:255601. [PMID: 33848988 DOI: 10.1088/1361-648x/abf7a2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 04/13/2021] [Indexed: 06/12/2023]
Abstract
By including the effect of a trap with characteristic energy given by the Fermi temperatureTFin a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a40K atomic Fermi gas. We also reproduce the experimental closed-channel fractionZacross the BEC-BCS crossover and into the BCS regime of a6Li atomic Fermi gas. We obtain the expected behaviorZ∝TFat unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of theZdependency onTFon the BCS side, where a significant quantitative discrepancy between experimental data and theory's predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity betweenZandTFpredicted by our model for a40K atomic Fermi gas.
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Affiliation(s)
- Eloisa Cuestas
- Facultad de Matemática, Astronomía, Física y Computación (FaMAF), Universidad Nacional de Córdoba (UNC), Av. Medina Allende s/n, Ciudad Universitaria, X5000HUA, Córdoba, Argentina
- Instituto de Física Enrique Gaviola (IFEG), Consejo de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), Córdoba, Argentina
| | - Ana P Majtey
- Facultad de Matemática, Astronomía, Física y Computación (FaMAF), Universidad Nacional de Córdoba (UNC), Av. Medina Allende s/n, Ciudad Universitaria, X5000HUA, Córdoba, Argentina
- Instituto de Física Enrique Gaviola (IFEG), Consejo de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), Córdoba, Argentina
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