Interpretable machine learning analysis of quantum gas microscopy data of doped Fermi-Hubbard model

Exploring the phase diagram of the Fermi-Hubbard model is among the key motivations of quantum simulation experiments. We apply the Hybrid-CCNN [1] approach to quantum gas microscopy data of the Fermi Hubbard model across a large doping range. The Hybrid-CCNN approach combines unbiased unsupervised machine learning with feature revealing supervised machine learning. The unsupervised learning stage identifies three different regimes: the magnetic polaron regime at low to intermediate dopings, and the Fermi liquid regime at high dopings, consistent with the manual analysis based on target correlation functions[2]. Moreover, unsupervised learning identifies the cross-over regime [2] as a distinct region of the phase space. The feature analysis using interpretable supervised learning techniques reveals characteristics unique to this intermediate phase. We discuss theoretical implications of the machine learning findings.

[1] Miles, C., Bohrdt, A., Wu, R. et al. Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data. Nat Commun 12, 3905 (2021). https://doi.org/10.1038/s41467-021-23952-w

[2] Koepsell, Joannis, et al. "Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid." Science 374.6563 (2021): 82-86.