Higher-order correlations in the Fermi-Hubbard model

Traditionally, one and two-point correlation functions are used to characterize many-body systems.
In strongly correlated quantum materials these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can even be dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. In this talk I will discuss recent results on higher-order correlations in doped quantum anti-ferromagnets. We consider a single mobile hole in the t − J model using DMRG, and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant.
We furthermore study the doping dependence of different multi-point correlations between spins and holes at temperatures around the superexchange energy in a quantum gas microscope and observe the crossover from a magnetic polaron regime into a Fermi liquid.