Recent progress in computational studies of the two-dimensional Hubbard model

S. Sorella, Stefano Baroni A, Roberto Car +3 more

Alberto Parola, Sandro Sorella, Stefano Baroni A +3 more

Luhang Yang, Adrian E. Feiguin, Thomas Devereaux +1 more

The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism, ferromagnetism, superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.

Minoru Takahashi

Journal of the Physical Society of Japan 59 (1990) pp. 1357-1365 Thermodynamic Quantities of the One-Dimensional Hubbard Model at Finite Temperatures Tatsuya Usuki, Norio Kawakami and Ayao Okiji Journal of the Physical Society of Japan 60 (1991) pp. 1460-1463 Temperature Dependence of Spin Correlation Length of Half-Filled One-Dimensional Hubbard Model Hirokazu Tsunetsugu Journal of the Physical Society of Japan 60 (1991) pp. 3754-3760 Dynamical Propertiesof the One-Dimensional Hubbard Model–A Numerical Study– Hiromi Otsuka Journal of the Physical Society of Japan 64 (1995) pp. 4331-4344 Logarithmic Correction Terms of the Magnetic Susceptibility in Highly Correlated Electron Systems Kenro Kawano and Minoru Takahashi Journal of the Physical Society of Japan 70 (2001) pp. 3398-3418 Filling-Control Metal-Insulator Transition in the Hubbard Model Studied by the Operator Projection Method Shigeki Onoda and Masatoshi Imada Progress of Theoretical Physics Vol. 47 No. 1 (1972) pp. 69-82 One-Dimensional Hubbard Model at Finite Temperature Minoru Takahashi Progress of Theoretical Physics Vol. 48 No. 6 (1972) pp. 2171-2186 Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model. II Hiroyuki Shiba Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 103-114 Low-Temperature Specific-Heat of One-Dimensional Hubbard Model Minoru Takahashi Progress of Theoretical Physics Vol. 53 No. 4 (1975) pp. 955-969 Possible Phases and Some Properties of the One-Dimensional Metal with the Half-Filled Band Minoru Kimura Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1039-1049 Long-Range Orders in Ground States and Collective Modes in One- and Two-Dimensional Models Satoshi Takada Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 758-769 Magnetic Susceptibility of the Strongly Correlated Hubbard Model Kenn Kubo

Yuan-Yao He, Bing Yang

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.

Guoshun Feng