Fermi-Hubbard model is a fundamental lattice model describing correlated electron systems in condensed matter physics and is closely related to high-temperature superconductivity. In recent years, cold-atom quantum simulations have become an important paradigm for studying the Fermi-Hubbard model, and advances in quantum many-body computations have contributed to our understanding of its fundamental properties. Notably, a recent ultracold-atom experiment achieving the well-known antiferromagnetic (AFM) phase transition in the three-dimensional (3D) Hubbard model represents a key step in quantum simulation, laying a foundation for exploring the link between the quantum magnetism and high-temperature superconductivity. In this paper, the experimental and theoretical research progress of Fermi-Hubbard model in 3D systems is reviewed, the development history and present status in this field are discussed, and the future development direction is also prospected. The paper is organized as follows. To begin with, recent progress of observing AFM phase transitions in the 3D Hubbard model is reviewed, focusing on an ultracold-atom experiment conducted by the research group at the University of Science and Technology of China (USTC). Next, a theoretical introduction to the fundamental properties of the 3D Hubbard model is provided, in which prior theoretical studies is summarized, the current research status is outlined, and some unresolved or under-explored problems are discussed. In Section 3, the quantum simulation of the Hubbard model using ultracold atoms in optical lattices is discussed, and the basic principle, historical developments and key challenges are outlined. The USTC team overcame these challenges through innovative techniques such as atom cooling, large-scale uniform box traps, and precise measurements of the AFM structure factor. Their work successfully confirms the AFM phase transition via the critical scaling analysis. Finally, the significance of this achievement is emphasized, and the future research prospects of the 3D Hubbard model are discussed, including experimental studies on the doped regions and related theoretical benchmarks.Fermi-Hubbard model is a fundamental lattice model describing correlated electron systems in condensed matter physics and is closely related to high-temperature superconductivity. In recent years, cold-atom quantum simulations have become an important paradigm for studying the Fermi-Hubbard model, and advances in quantum many-body computations have contributed to our understanding of its fundamental properties. Notably, a recent ultracold-atom experiment achieving the well-known antiferromagnetic (AFM) phase transition in the three-dimensional (3D) Hubbard model represents a key step in quantum simulation, laying a foundation for exploring the link between the quantum magnetism and high-temperature superconductivity. In this paper, the experimental and theoretical research progress of Fermi-Hubbard model in 3D systems is reviewed, the development history and present status in this field are discussed, and the future development direction is also prospected. The paper is organized as follows. To begin with, recent progress of observing AFM phase transitions in the 3D Hubbard model is reviewed, focusing on an ultracold-atom experiment conducted by the research group at the University of Science and Technology of China (USTC). Next, a theoretical introduction to the fundamental properties of the 3D Hubbard model is provided, in which prior theoretical studies is summarized, the current research status is outlined, and some unresolved or under-explored problems are discussed. In Section 3, the quantum simulation of the Hubbard model using ultracold atoms in optical lattices is discussed, and the basic principle, historical developments and key challenges are outlined. The USTC team overcame these challenges through innovative techniques such as atom cooling, large-scale uniform box traps, and precise measurements of the AFM structure factor. Their work successfully confirms the AFM phase transition via the critical scaling analysis. Finally, the significance of this achievement is emphasized, and the future research prospects of the 3D Hubbard model are discussed, including experimental studies on the doped regions and related theoretical benchmarks.

Acta Physica SinicaDec 9, 20242 citations

Quantum simulations with ultracold atoms

Nikolay Prokofiev

Bulletin of the American Physical SocietyFeb 29, 20120 citations

Simulation of exact quantum Ising models with a Mott insulator of paired atoms

Ren Liao, Jingxin Sun, Pengju Zhao +8 more

Quantum simulation of the $XXZ$ model with a two-component Bose- or Fermi-Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here, we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic models become the exact quantum Ising models in a one-dimensional (1D) or two-dimensional (2D) lattice. Meanwhile, we analyzed an experimentally achievable three-component Fermi-Hubbard model of $^{6}\mathrm{Li}$ with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetism of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. Our results may be useful for experimental investigations of the quantum phase transition and quantum criticality of the 1D and 2D quantum Ising models with ultracold neutral atoms.Quantum simulation of the $XXZ$ model with a two-component Bose- or Fermi-Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here, we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic models become the exact quantum Ising models in a one-dimensional (1D) or two-dimensional (2D) lattice. Meanwhile, we analyzed an experimentally achievable three-component Fermi-Hubbard model of $^{6}\mathrm{Li}$ with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetism of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. Our results may be useful for experimental investigations of the quantum phase transition and quantum criticality of the 1D and 2D quantum Ising models with ultracold neutral atoms.

arXiv:2112.06422Physical Review ANov 9, 20223 citations

Quantum simulation with ultracold atoms

Laurent Sanchez-Palencia

Aug 1, 20200 citations

Observation of emergent scaling of spin–charge correlations at the onset of the pseudogap

Thomas Chalopin, Petar Bojović, Si Wang +12 more

In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual "pseudogap" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multipoint correlation functions up to fifth order, we uncover a universal scaling behavior in magnetic and higher-order spin-charge correlations characterized by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature [Formula: see text]. Our quantitative findings reveal a qualitative behavior of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way toward the exploration of charge pairing and collective phenomena expected at lower temperatures.In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual "pseudogap" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multipoint correlation functions up to fifth order, we uncover a universal scaling behavior in magnetic and higher-order spin-charge correlations characterized by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature [Formula: see text]. Our quantitative findings reveal a qualitative behavior of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way toward the exploration of charge pairing and collective phenomena expected at lower temperatures.

arXiv:2412.17801Proceedings of the National Academy of SciencesJan 23, 202616 citations

Quantum simulation of the

XXZ

model with a two-component Bose- or Fermi-Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here, we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic models become the exact quantum Ising models in a one-dimensional (1D) or two-dimensional (2D) lattice. Meanwhile, we analyzed an experimentally achievable three-component Fermi-Hubbard model of

^{6}\mathrm{Li}

with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetism of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. Our results may be useful for experimental investigations of the quantum phase transition and quantum criticality of the 1D and 2D quantum Ising models with ultracold neutral atoms.