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Nature

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

Published Jul 10, 2024• 66 citations
Publisher
DOI
10.1038/s41586-024-07689-2

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The study by Shao et al.1 marks a critical advancement in quantum simulations by reporting the first experimental observation of the antiferromagnetic (AFM) phase transition in a 3D fermionic Hubbard model (FHM) using ultracold lithium-6 atoms. This experiment bridges a significant gap in our understanding of strongly correlated systems and provides a new platform to explore low-temperature quantum phases. This commentary will analyze the results, place them in the context of ongoing research, and discuss their broader implications for the field of quantum materials and technologies.
Abstract The celebrated antiferromagnetic (AFM) phase transition was realized in a most recent optical lattice experiment for the 3D fermionic Hubbard model [ Shao et al . Nature 632 267 (2024) ]. Despite this important progress, it was observed that the AFM structure factor (and also the critical entropy) reaches its maximum at an interaction strength U / t ≃ 11.75, which is significantly larger than the theoretical prediction of U / t ≃ 8. Here, we resolve this discrepancy by studying the interplay between the thermal entropy, density disorder, and antiferromagnetism in the half-filled 3D Hubbard model, using numerically exact auxiliary-field quantum Monte Carlo simulations. We have achieved an accurate entropy phase diagram, enabling us to simulate arbitrary entropy path on the temperature-interaction plane and track experimental parameters effectively. We find that above the discrepancy can be quantitatively explained by the entropy increase associated with increasing interaction strength in experiments, and together with the lattice density disorder present in the experimental setup. We further investigate the entropy dependence of double occupancy and predict universal behaviors that could serve as valuable probes in future optical lattice experiments.
We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $\ensuremath{\pi}$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-range AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)-dimensional Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in the birefringent Dirac fermion system. It is found that the critical interaction strength Uc{U}_{c}Uc​ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions and may be observed using ultracold atoms in an optical lattice.