Tensor network study of the spin-1/2 Heisenberg antiferromagnet on the shuriken lattice

We investigate the ground state of the spin S = 1/2 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 E-0/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, 1/3, and 2/3 magnetization plateaus. The 1/3 and 2/3 plateau states respect translation and point group symmetries and feature loop-four plaquette resonances.

Automated summary

We investigate the ground state of the spin S = 1/2 Heisenberg antiferromagnet on the shuriken lattice, and found that a valence bond crystal with resonances over length six loops emerges as the ground state, yielding the lowest reported estimate of the ground state energy for this model. We also study the model in the presence of an external magnetic field and find the emergence of 0, 1/3, and 2/3 magnetization plateaus, with the 1/3 and 2/3 plateau states respecting translation and point group symmetries and featuring loop-four plaquette resonances.