Fig. 3: Significance of longer ranged couplings.

By evaluating the conditioned correlators, Eqs. (4) and (5), we estimate the strengths of longer ranged couplings up to J₄. In units of the strongest interaction \({J}_{1}^{x}\), first order diagonal bonds J₂ are of the order of ~10%, whereas couplings J₃ reach relative magnitudes of a few percent. Due to the finite system size, J₃ (J₄) and higher order couplings drop to zero for n^h = 0.05 (n^h = 0.1), as the corresponding conditioned probabilities Eq. (5) vanish for a single (two) hole(s) per leg.