Classifying Snapshots of the Doped Hubbard Model with Machine Learning

Quantum gas microscopes for ultracold atoms provide real-space snapshots of complex many-body systems with single site resolution. We use machine learning techniques to analyse and classify such snapshots of ultracold atoms. Specifically, we study the two-dimensional Fermi-Hubbard model, which is believed to capture the rich physics of high-temperature superconductivity and other phases such as the strange metal, stripe, antiferromagnet, or pseudo-gap phase. While a large number of theories exist to describe this system, each with its own merits, a unifying analytic understanding is still lacking. We compare the data from an experimental realization of the two-dimensional Fermi–Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type, and the geometric string theory, describing a state with hidden spin order. This method considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory that is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights.

[1] A. Bohrdt et al., Nature Physics Vol. 15, pp. 921–924 (2019)