At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultracold atoms, frustrated magnets, and quantum moiré materials, their unbiased presence remains elusive in microscopic two-dimensional lattice models. Here, we show, by means of large-scale quantum Monte Carlo simulations of correlated electrons on the $\pi$-flux square lattice subjected to plaquette Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and a columnar valence bond solid at finite interaction and a possible Dirac QSL at the infinite yet tractable interaction limit emerge in a coherent sequence. These unexpected quantum states reside in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization, and the dynamic coupling between emergent matter and gauge fields and will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.

中文翻译：

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具有斑块相互作用的狄拉克费米子。二、具有 Gross-Neveu 临界和量子自旋液体的 SU(4) 相图

在足够低的温度下，相互作用的电子系统倾向于发展秩序。例外是量子临界点 (QCP) 和量子自旋液体 (QSL)，其中波动阻止高度纠缠的量子物质在最低温度下进入有序状态。虽然这些状态的分支可能已经出现在高温超导体、超冷原子、受挫磁体和量子莫尔材料中，但它们的无偏存在在微观二维晶格模型中仍然难以捉摸。在这里，我们通过对相关电子的大规模量子蒙特卡罗模拟展示了$\pi$-通量方形晶格受到斑块哈伯德相互作用，在有限相互作用下分离无质量狄拉克费米子和柱状价键固体的 Gross-Neveu QCP 和在无限但易于处理的相互作用极限下的可能狄拉克 QSL 以连贯序列出现。这些意想不到的量子态存在于这个看起来很简单的模型中，统一了包括涌现对称性、去限制分馏以及涌现物质和规范场之间的动态耦合在内的成分，并将对量子多体理论和对上述实验系统的理解产生深远的影响.