近日，美国伊利诺伊大学厄巴纳-香槟分校Philip W. Phillips团队实现了将哈伯德模型扭曲成混合动量的Hatsugai-Kohmoto模型。相关论文于2025年11月27日发表在《自然—物理学》杂志上。

哈伯德模型是研究强关联电子材料（如铜氧化物超导体）的标准理论工具。然而，由相互作用驱动的现象（如进入强关联Mott绝缘体相的转变）难以用传统理论方法处理。Hatsugai–Kohmoto模型虽可精确求解，却展现出类似的Mott物理特性。

研究组展示了如何将Hatsugai–Kohmoto模型连续变形为Hubbard模型。关键方法是系统性地重新引入原Hatsugai–Kohmoto模型忽略的所有动量混合过程。具体而言，通过将n个动量分组到一个单元并进行杂化，构建了动量混合型Hatsugai–Kohmoto模型。在一维情况下，仅用10个混合动量即可将Hubbard模型的Bethe假设法基态能量重现精度控制在1%以内。其收敛速度按1/n²标度，显著优于传统有限簇方法的线性反比关系。正方晶格的计算结果亦以少量混合动量复现了当前最先进模拟的所有已知特征。因此，动量混合型Hatsugai–Kohmoto模型为研究强关联量子物质提供了新的理论工具。

附：英文原文

Title: Twisting the Hubbard model into the momentum-mixing Hatsugai–Kohmoto model

Author: Mai, Peizhi, Zhao, Jinchao, Tenkila, Gaurav, Hackner, Nico A., Kush, Dhruv, Pan, Derek, Phillips, Philip W.

Issue&Volume: 2025-11-27

Abstract: The Hubbard model is a standard theoretical tool for studying materials with strong electron–electron interactions, such as cuprate superconductors. Unfortunately, interaction-driven phenomena, such as a transition into the strongly correlated Mott insulator phase, are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai–Kohmoto model displays similar Mott physics. Here we show how the Hatsugai–Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically reintroduce all the momentum mixing that the original Hatsugai–Kohmoto model omits. This can be accomplished by grouping n momenta into a cell and hybridizing them, resulting in the momentum-mixing Hatsugai–Kohmoto model. We recover the Bethe ansatz ground-state energy of the one-dimensional Hubbard model to within 1% from only ten mixed momenta. Overall, the convergence scales as 1/n2 as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all the known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe that the momentum-mixing Hatsugai–Kohmoto model offers an alternative tool for strongly correlated quantum matter.

DOI: 10.1038/s41567-025-03095-1

Source: https://www.nature.com/articles/s41567-025-03095-1