Machine learning applied to the doped Hubbard model

In our recent paper, we analyze snapshots of the doped Fermi-Hubbard model by a convolutional neural network. First, we train the network to distinguish between multiple theoretical models. Then we feed actual experimental data from a quantum gas microscope into the network, and classify this data into one of the theoretical categories. This generic procedure allows for an unbiased distinction between different theoretical models.

Specifically, we compare the geometric string approach, where anti-ferromagnetic order is hidden by the hole motion, to π-flux RVB predictions for the doped Hubbard model. Up to ~ 15 % doping, we find that the experiment resembles the geometric string theory significantly more closely.

Our work has been published in Nature Physics:

A. Bohrdt, C. S. Chiu, G. Ji, M. Xu, D. Greif, M. Greiner, E. Demler, F. Grusdt and M. Knap, "Classifying Snapshots of the Doped Hubbard Model with Machine Learning", Nature Physics (2019), online version.

See also: Which one is the perfect quantum theory?

In a closely related work, our colleagues from Hamburg analyzed experimental images using an artificial neural network. They demonstrated that the machine learning method is able to identify the Chern number in a Haldane-like lattice model - see Rem et al., Nature Physics (2019).