In a study published online in NatureA research team led by Professor PAN Jianwei, Professor CHEN Yuao, and Professor YAO Xingcan from the University of Science and Technology of China (USTC), Chinese Academy of Sciences, has observed the antiferromagnetic phase transition in a large-scale quantum simulator of the fermionic Hubbard model (FHM) for the first time. This study highlights the advantages of quantum simulation. It marks an important first step toward obtaining the low-temperature phase diagram of the FHM and understanding the role of quantum magnetism in the mechanism of high-temperature superconductivity.
Strongly correlated quantum materials, such as high-temperature superconductors, are of scientific importance and have potential economic benefits. However, the physical mechanisms underlying these materials remain unclear, posing challenges for their preparation and large-scale application. The FHM, a simplified representation of electron behaviors in a lattice, captures a wide range of physics related to strong correlations, similar to those observed in quantum materials, and is thus expected to potentially offer solutions for understanding the mechanism of high-temperature superconductivity.
The study of the FHM is fraught with challenges. There is no exact analytical solution for this model in two and three dimensions, and due to the high computational complexity, even the most advanced numerical methods can only explore limited parameter spaces. Moreover, theoretical studies suggest that even a universal digital quantum computer would struggle to solve this model accurately.
It is widely accepted that quantum simulation, using ultracold fermionic atoms in optical lattices, may be the key to mapping the low-temperature phase diagram of the FHM. To this end, realizing the antiferromagnetic phase transition and reaching the FHM ground state at half-filling are the most important steps. Such an achievement would validate two key capabilities of the quantum simulator: establishing a large-scale, spatially homogeneous optical lattice for uniform Hubbard parameters, and maintaining a system temperature significantly below the Néel temperature, the antiferromagnetic phase transition temperature, both of which are essential to explore the role of quantum magnetic fluctuations in the mechanism of high-temperature superconductivity.
However, the difficulty of cooling fermionic atoms and the inhomogeneity introduced by a standard Gaussian profile lattice laser have hampered the realization of the antiferromagnetic phase transition in previous quantum simulation experiments. To address these challenges, the team, building on their previous achievements in preparing and studying strongly interacting homogeneous Fermi gases in a box potential (Science, Nature), developed an advanced quantum simulator by combining the generation of a low-temperature homogeneous Fermi gas in a box trap with the demonstration of a flat-top optical lattice with uniform site potentials.
This quantum simulator contains about 800,000 lattice sites, about four orders of magnitude more than current experiments with several dozen sites, and features uniform Hamiltonian parameters with temperatures well below the Néel temperature. Exploiting this setup, the team fine-tuned the interaction strength, temperature, and doping concentration to approach their respective critical values, and directly observed conclusive evidence for the antiferromagnetic phase transition, i.e., the power-law divergence of the spin structure factors, with a critical exponent of 1.396 relative to Heisenberg universality.
This work advances the understanding of quantum magnetism and lays the foundation for further solving the FHM and obtaining its phase diagram at low temperatures. Notably, experimental results deviating from the half-filling condition have already exceeded the capabilities of current classical computing, demonstrating the advantages of quantum simulation for solving key scientific problems.
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