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Traditionally one and two-point correlation functions are used tocharacterize many-body systems. In strongly correlated quantum materials, suchas the doped 2D Fermi-Hubbard system, these may no longer be sufficient becausehigher-order correlations are crucial to understanding the character of themany-body system and can be numerically dominant. Experimentally, suchhigher-order correlations have recently become accessible in ultracold atomsystems. Here we reveal strong non-Gaussian correlations in doped quantumanti-ferromagnets and show that higher order correlations dominate overlower-order terms. We study a single mobile hole in the $t-J$ model using DMRG,and reveal genuine fifth-order correlations which are directly related to themobility of the dopant. We contrast our results to predictions using modelsbased on doped quantum spin liquids which feature significantly reducedhigher-order correlations. Our predictions can be tested at the lowestcurrently accessible temperatures in quantum simulators of the 2D Fermi-Hubbardmodel. Finally, we propose to experimentally study the same fifth-orderspin-charge correlations as a function of doping. This will help to reveal themicroscopic nature of charge carriers in the most debated regime of the Hubbardmodel, relevant for understanding high-$T_c$ superconductivity.

Dominant fifth-order correlations in doped quantum anti-ferromagnets