Structural complexity of projective measurements of the SU(3) Fermi Hubbard model

Analog quantum simulations of the Fermi-Hubbard Model (FHM) provide a useful platform for understanding correlated fermions in lattice systems. Quantum gas microscopy, and in particular, spin-resolved projective measurements (or snapshots), have played a crucial role in quantifying correlation functions and thus enabling insights into physical phenomena in the FHM. In this work, we mimic spin-resolved projective measurements using mean-field calculations to find the ground state at different interaction strengths at one-third filling the two-dimensional SU(3) FHM in the square lattice. We employ the multiscale structural complexity on these snapshots to locate the phase boundaries of the model at T=0. We study the dependence of structural complexity on the geometry of the coarse-graining window, systematically varying coarse-graining lattice dimensions. We also explore its connection with the entanglement entropy, as they both capture relevant correlations across different length scales in the model. In this presentation we analyze our main results and discuss the feasibility of using the structural complexity as a flexible framework for diagnosing phase boundaries in experiments with ultra cold atoms in optical lattices.