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

Understand

The spin-$1/2$ model system with antiferromagnetic (AF) couplings on a $J_1$-$J_2$ 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 ($J_1<J_2$).
• Specifically, we find the long-sought crossed-dimer valence bond solid (VBS) state to be the ground state at $J_1\lesssim J_2$, while various 1D AF correlated states take over the rest.
• We verify the stability of the VBS state against nematic perturbation.