Néel and valence-bond crystal phases of frustrated two-dimensional Heisenberg models

I use an improved version of the two-step density-matrix renormalization group method to study ground-state properties of the two-dimensional (2D) Heisenberg model on the checkerboard lattice. In this version, the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as J2 increases are (i) Néel with Q= (π,π), (ii) a valence-bond crystal (VBC) of plaquettes, (iii) Néel with Q= (π/2,π), and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point J2 = J1, the ground state is made of weakly interacting plaquettes with a large gap Δ≈0.67 J1 to triplet excitations. The same approach is also applied to the J1 - J2 model. There is no evidence of a columnar dimer phase in the highly frustrated regime.