Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the $t-J$ model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-$T_c$ superconductivity.

中文翻译：

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掺杂量子反铁磁体中的主要五阶相关性

传统上，一点和两点相关函数用于表征多体系统。在强相关的量子材料（例如掺杂的2D费米-哈伯德系统）中，这些可能不再足够，因为高阶相关对理解多体系统的特性至关重要，并且在数值上占主导地位。实验上，最近在超冷原子系统中可以访问这种高阶相关性。在这里，我们揭示了掺杂量子反铁磁体中的强非高斯相关性，并表明高阶相关性在低阶项上占主导地位。我们研究了$Ť-Ĵ$使用密度矩阵重归一化模型进行建模，并揭示与掺杂剂迁移率直接相关的真正的五阶相关性。我们将结果与使用基于掺杂量子自旋液体的模型进行的预测进行对比，该模型具有明显降低的高阶相关性的特征。我们的预测可以在2D Fermi-Hubbard模型的量子仿真器中当前可以达到的最低温度下进行测试。最后，我们建议通过实验研究作为掺杂函数的相同的五阶自旋电荷相关性。这将有助于揭示在辩论最激烈的哈伯德模型中，电荷载子的微观性质，与理解高${Ť}_C$ 超导。