3 Figure 1: (Color online). (a) Spin-structure factor S ( q x ) vs. q x for the two-leg ladder system with sizes L = 12 , 16, and 24, and for density ρ = 2, J = 1 . 5, and U eff = − 0 . 5. (b) S ( π, 0) as a function of J for ladders with linear sizes L = 8 and U eff = − 0 . 5. The inset shows the magnitude of this peak as a function of U eff , for the coupling J = 1 . 5. (c) Spin-spin correlation C spin ( j ) vs. j along the long ladder direction, for a system with size L = 24, and for the couplings U eff = − 0 . 5 and J = 1 . 5. The dashed curve is a fit given by Eq. (5). 1 1.5 2 q$_{x}$/ 0 2 4 6 8 10 S(q x ) 2x12 q$_{y}$=0 2x12 q$_{y}$= 2x16 q$_{y}$=0 2x16 q$_{y}$= 2x24 q$_{y}$=0 2x24 q$_{y}$= J=1.5 U$_{eff}$=-0.5  (a) 0.5 1 1.5 2 J 2 3 4 5 S( -2 -1 0 1 2 U$_{eff}$ 4.88 4.92 4.96 5 U$_{eff}$=-0.5 2x8 (b) J=1.5 0 5 10 15 j -0.4 -0.2 0 0.2 0.4 C spin (j) DMRG fit J=1.5 U$_{eff}$=-0.5  (c) 2x24 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: 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. 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 III. RESULTS A. Magnetic Properties at ρ = 2 S ( q ) = 1 6 L ∑ j,j ′ ,λ,λ ′ e iq$_{x}$ ( j − j ′ ) e iq$_{y}$ ( λ − λ ′ $^{)}$〈 S$_{j,λ}$ · S$_{j}$ ′ ,λ ′ 〉 , (3)