Fermionic Hubbard quantum simulator observes antiferromagnetic phase transition

In a study published in Naturea research team has observed the antiferromagnetic phase transition for the first time within a large-scale quantum simulator of the fermionic Hubbard model (FHM).

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. The team was led by Prof. Pan Jianwei, Prof. Chen Yuao and Prof. Yao Xingcan from the University of Science and Technology of China (USTC) of the Chinese Academy of Sciences.

Strongly correlated quantum materials such as high-temperature superconductors are of scientific interest and have potential economic benefits. However, the physical mechanisms underlying these materials remain unclear, posing challenges for their large-scale preparation and application.

The FHM, a simplified representation of the behavior of electrons in a lattice, encompasses a wide range of physical aspects associated with strong correlations, similar to those observed in quantum materials. It is therefore thought that the FHM may provide clues to understanding the mechanism of high-temperature superconductivity.

The study of FHM faces challenges. There is no exact analytical solution for this model in two and three dimensions, and due to its high computational complexity, even the most advanced numerical methods can only explore limited parameter spaces. Furthermore, theoretical studies suggest that even a universal digital quantum computer would struggle to solve this model accurately.

It is generally accepted that quantum simulation using ultracold fermionic atoms in optical lattices can be the key to mapping the low-temperature phase diagram of the FHM. For this, realizing the antiferromagnetic phase transition and reaching the ground state of the FHM at half-filling are the key 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 lower than the Néel temperature, the antiferromagnetic phase transition temperature. Both are essential for investigating 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 antiferromagnetic phase transition in previous quantum simulation experiments. To address these challenges, based on their previous achievements of preparing and investigating homogeneous strongly interacting Fermi gases in a box potential, the team developed an advanced quantum simulator by combining the generation of a homogeneous Fermi gas at low temperature 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 larger than current experiments with a few tens of sites, and exhibits uniform Hamiltonian parameters with temperatures significantly lower than the Néel temperature.

Using this setup, the team was able to fine-tune the interaction strength, temperature, and doping concentration to approach their respective critical values. This allowed them to directly observe decisive evidence for the antiferromagnetic phase transition, i.e., the power-law divergence of the spin structure factors, with a critical exponent of 1.396 with respect to Heisenberg universality.

This work advances the understanding of quantum magnetism and lays the foundation for further solution of the FHM and obtaining the low-temperature phase diagram. In particular, the experimental results deviating from the half-filling condition have already surpassed the capabilities of current classical computer technology, demonstrating the advantages of quantum simulation in tackling important scientific problems.