We investigate the ground state of the spin S=12 Heisenberg antiferromagnet on the shuriken lattice, also in the presence of an external magnetic field. To this end, we employ two-dimensional tensor network techniques based on infinite projected entangled pair and simplex states considering states with different sizes of the unit cells. We show that a valence bond crystal with resonances over length six loops emerges as the ground state (at any given finite bond dimension) yielding the lowest reported estimate of the ground state energy E0/J=−0.4410±0.0001 for this model, estimated in the thermodynamic limit. We also study the model in the presence of an external magnetic field and find the emergence of 0, 13, and 23 magnetization plateaus. The 13 and 23 plateau states respect translation and point group symmetries and feature loop-four plaquette resonances.
