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We have investigated the model defined above using a two-leg ladder of size 2 × L , by means of the Density Ma- trix Renormalization Group (DMRG) technique, 29 un- der open boundary conditions (OBC), and keeping up to m =1400 states per block in the final DMRG sweep. We have carried out ∼ 6 − 13 sweeps, and the discarded weight was typically 10 − 6 10 − 9 at the final sweep. In our DMRG procedure, the center blocks are composed of 16 states. We have used a FORTRAN DMRG code to calculate most results, and a C++ DMRG code for additional validation. 30 We have also confirmed some of our results against Lanczos Exact Diagonalization tech- niques, when possible. 

In this work, we will focus on the region of Hubbard and Hund parameters where U$_{eff}$ ≡ U − 3 J = U ′ − J < 0, although a few results for positive values of U$_{eff}$ will be presented as well. As shown below, in the region where U$_{eff}$ < 0 there is a robust evidence of binding of holes/electrons close to density ρ = 2. In this regime U ′ < J . This inequality may not seem realistic at first sight, since the on-site spin triplet formation favored by J (Hund’s rules) has its origin in the alleviation of the Coulombic energy penalization caused by U $^{′}$. However, while in the full five-orbital model for Fe-based com- pounds U ′ < J is unphysical for the reason stated above, the two-orbital model is an effective model and it is un- clear how the main parameters are affected by the pro- jection from five to two orbitals. Thus, the regime U ′ comparable to J may not be unrealistic. Clearly addi- tional investigations are needed to analyze if this regime of couplings is of relevance for real materials, such as heavy fermions. Ab-initio calculations are needed for this purpose (beyond the scope of the present analysis). 

Let us start our analysis by focusing on the density ρ = 2. To investigate the magnetic order at this density, the Fourier transform of the real-space spin-spin correlation function was measured: 

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where S$_{j,λ}$ = S$_{j,x,λ}$ + S$_{j,y,λ}$ . In Fig. 1(a), the spin struc- ture factor S ( q ) of the two-leg model is presented for several system sizes. As can be observed in this figure, there is a robust peak at wavevector q =( π, 0), showing the tendency toward a stripe-like AFM order. This is the analog of the magnetic order found in pnictides but us- ing a two-leg ladder geometry. Similar results, obtained with Exact Diagonalization on small clusters, were re- ported before. 12,13 Note that the peak increases with the system size, suggesting the development of a true long- range magnetic order in systems with a higher dimension. 

## A. Magnetic Properties at ρ = 2 

## III. RESULTS 

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The results for the spin structure factor show that along the y ( x )-axes the spins are aligned following a ferromagnetic (AFM) order, at least at short distances. This stripe-like AFM structure is present in a wide range of parameters, as shown in Fig. 1(b) (inset), including 

