Tensor networ simulation of phase diagram of frustrated J1-J2 Heisenberg model on a checkerboard lattice

We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic J1-J2 Heisenberg model on a checkerboard lattice. The simulation indicates a Neel ordered phase when J2 $<$ 0.88J1, a plaquette valence bond solid state when 0.88 $<$ J2/J1 $<$ 1.11, and a stripe phase when J2 $>$ 1.11J1, with two first-order transitions across the phase boundaries. The calculation shows the cross-dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.