Quantum gas microscopy has evolved into a powerful tool for exploring strongly correlated quantum systems. However, discrimination phases with topological or off-diagonal long-range order require the ability to extract these correlations from site-resolved measurements. Here, the multiscale complexity measure is the transition to and from the coupled ordered wave phase of a one-dimensional extended Hubbard model with off-diagonal order parameters sandwiched between the diagonal charge and spin density wave phases. indicates that the can be identified. Diagonal descriptor only. The model can be directly studied in the thermodynamic limit using the recently developed variational uniform matrix product-state algorithm, emulating experimentally accessible projective measurements, from degenerate ground states associated with global spin rotation. Pull out the sample. Our results have important implications for the study of exotic phases using optical lattice experiments.