Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation

The spin-1/2 model system with antiferromagnetic (AF) couplings on a J₁-J₂ checkerboard lattice, known as the planar pyrochlore model, is strongly frustrated and associated with a two-to-one dimensional crossover. Using the Projected Entangled Simplex States tensor network ansatz, we identify a large number of nearly degenerate states in the frustrated region $J₁<J₂$. Specifically, we find the long-sought crossed-dimer valence bond solid (VBS) state to be the ground state at J_1lesssim J₂, while various 1D AF correlated states take over the rest. We verify the stability of the VBS state against nematic perturbation. The corresponding bosonic picture provides an intuitive understanding of the low-energy physics. Particularly, it predicts weaker VBS states in the easy-plane limit, which we confirm numerically. Our results clarify the most essential ground state properties of this interesting system and demonstrate the usefulness of bosonic picture in dealing with frustrated magnetism.