Structural complexity of Fermi Hubbard model snapshots

The structural complexity is a recently introduced unbiased measure to analyze images. This measure aggregates information about different scales present in the problem by performing a series of coarse-graining steps on concatenated samples, which at the end of the procedure produces a single number which encodes properties of the image whose connection the physics we wish to determine. In this work we study the evolution of the structural complexity in projective measurements (snapshots) of the two-dimensional Fermi Hubbard model across different filling fractions and temperatures spanning the antiferromagnetic regime and the strange metallic regions. We demonstrate that the complexity measure is linked to relevant physical observables of the model, such as the entropy and the double occupancy, and provides an immediately useful tool for ultra cold atom experiments. In addition, we further explore the application of this method to quantities other than projective measurements.