Fig. 5

Comparison with the J₁–J₂ model. a Comparison of the static SSF S(q) corresponding to the multi-orbital system vs results for the J₁–J₂ model with J₂/|J₁| = 1, calculated for L = 32 and L = 48, respectively. S(q) is normalized by the local magnetic moment squared S² = S(S + 1), where S² = 3/4 for the localized orbital and the J₁–J₂ result, and S² = 2²³ for the total SSF. b Acoustic mode of the dynamical SSF within the block-OSMP phase (the same results as in Fig. 2b) compared against the dispersion relation ω(q) of the J₁–J₂ model with |J₁| = J₂ = 0.6J_eff, where the effective spin-exchange energy scale is set to \(J_{{\mathrm{eff}}} = 4{\kern 1pt} t_{22}^2{\mathrm{/}}U\). The latter is obtained with the help of Lanczos diagonalization on a chain of 32 sites with periodic boundary conditions. c Dynamical SSF of the J₁–J₂ model with |J₁| = J₂ = 0.6J_eff as calculated using DMRG for a L = 48 chain