Optimized Gutzwiller projected states for doped antiferromagnets in Fermi-Hubbard simulators

In quantum many-body physics, one aims to understand emergent phenomena and the effects of strong interactions, ideally by developing a simple theoretical picture. Recently, progress in quantum simulators has enabled the measurement of site-resolved snapshots of Fermi-Hubbard systems at finite doping on square as well as triangular lattice geometries. These experimental advances pose the quest for theorists to analyze the ensuing data in order to gain insights into these prototypical strongly correlated many-body systems. Here, we employ machine learning techniques to optimize the mean-field parameters of a resonating valence bond (RVB) state through comparison with experimental data, thus determining a possible underlying simple model that is physically motivated and fully interpretable. We find that the resulting RVB states are capable of capturing two- as well as three-point correlations measured in experiments, even when they are not specifically used for the optimization. The analysis of the mean-field parameters and their doping dependence can be used to obtain physical insights and shed light on the nature of possible underlying quantum spin liquid states. Our results show that finite temperature data from Fermi-Hubbard quantum simulators can be well captured by RVB states. This work paves the way for a systematic analysis of data from numerical as well as quantum simulation of strongly correlated quantum many-body systems.