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Fermi-Hubbard model is a fundamental lattice model for describing correlated electron systems in condensed matter physics, with a profound connection to high-temperature superconductivity. In recent years, quantum simulation with cold atoms has emerged as an important paradigm for studying the Fermi-Hubbard model, while advancements in quantum many-body computations have contributed to our understanding of its fundamental properties. Notably, a recent ultracold-atom experiment achieved the celebrated antiferromagnetic (AFM) phase transition in the three-dimensional (3D) Hubbard model, representing a crucial step in quantum simulation that establishes a foundation for exploring the connection between the quantum magnetism and high-temperature superconductivity. This paper reviews both the experimental and theoretical progress in studying the Fermi-Hubbard model, focusing primarily on 3D systems, discusses the history and current state of developments, and outlines future directions in this field.
The paper is organized as follows. We begin with a review of recent progress in observing AFM phase transitions in the 3D Hubbard model, focusing on an ultracold-atom experiment conducted by the research group at the University of Science and Technology of China (USTC). Next, we provide a theoretical introduction to the fundamental properties of the 3D Hubbard model. This includes a summary of prior theoretical studies, an overview of the current research landscape, and a discussion of unresolved or under-explored issues. In the third section, we discuss the quantum simulation of the Hubbard model using ultracold atoms in optical lattices, outlining the basic principle, historical developments and key challenges. The USTC team overcame these challenges with innovative techniques such as atom cooling, large-scale uniform box traps, and precise measurements of the AFM structure factor. Their work successfully confirmed the AFM phase transition via the critical scaling analysis. Finally, we highlight the significance of this achievement and discuss future research prospects for the 3D Hubbard model, including experimental studies on the doped regime and related theoretical benchmarks.-
Keywords:
- Fermi-Hubbard model /
- Quantum Simulation based on ultracold atoms /
- quantum many-body computation /
- antiferromagnetic phase transition
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